# Physics and Astronomy

MICHAEL R. BROWN, Professor of Physics and Chair ^{3}

AMY LISA GRAVES, Professor of Physics

PETER J. COLLINGS, Professor of Physics

FRANK A. MOSCATELLI, Professor of Physics

DAVID H. COHEN, Associate Professor of Astronomy

CATHERINE H. CROUCH, Associate Professor of Physics

CARL H. GROSSMAN, Associate Professor of Physics ^{1}

ERIC L.N. JENSEN, Professor of Astronomy and Interim Chair

MATTHEW MEWES, Visiting Assistant Professor of Physics

TRISTAN SMITH, Visiting Assistant Professor of Physics

DAVID SCHAFFNER, Post-Doctoral Research Scientist

MARY ANN KLASSEN, Senior Lecturer

ADAM NEAT, Lecturer

PAUL JACOBS, Instrumentation Technician

STEVEN PALMER, Machine Shop Supervisor

CAROLYN R. WARFEL, Administrative Assistant

^{1} Absent on leave, fall 2013.^{3} Absent on leave, 2013–2014.

The Physics and Astronomy Department teaches the concepts and methods that lead to an understanding of the fundamental laws governing the physical universe.

Emphasis is placed on quantitative, analytical reasoning, as distinct from the mere acquisition of facts. Particular importance is also attached to laboratory work because physics and astronomy are primarily experimental and observational sciences.

With the awareness that involvement in research is a major component in the education of scientists, the department offers a number of opportunities for students to participate in original research projects, conducted by members of the faculty, on campus.

Several research laboratories are maintained by the department to support faculty interests in the areas of laser physics, high-resolution atomic spectroscopy, plasma physics, nano physics, computer simulation, liquid crystals, and observational and theoretical astrophysics.

The department operates the Peter van de Kamp Observatory for student and faculty research, plus several small telescopes for instructional use. The observatory is equipped with a 61-cm reflecting telescope, a high-resolution spectograph, and a CCD camera for imaging and photometry. A monthly visitors’ night at the observatory is announced on the department website. Swarthmore College is also home to the historic Sproul 61-cm refracting telescope.

Two calculus-based introductory sequences are offered. PHYS 003 and 004 cover both classical and modern physics and is an appropriate introductory physics sequence for those students majoring in engineering, chemistry, and biology. PHYS 007 and 008, on the other hand, which are normally preceded by PHYS 005 are at a higher level. They are aimed toward students planning to do further work in physics or astronomy and are also appropriate for engineering and chemistry majors. The sequence of courses from PHYS 005 to PHYS 018 is designed to provide a comprehensive introduction to the major topics and mathematical tools of physics.

Additional information is available at www.swarthmore.edu/physics.

### The Academic Program

In order to receive a degree from Swarthmore as a physics, astrophysics, or astronomy major, a student must have taken and satisfactorily passed one of the programs described below. In the Physics and Astronomy Department, the seminar is the standard format for most junior and senior level work. All prospective majors and minors in the department should realize this when planning programs. The seminars are open to all students, both honors and course majors.

#### Core Programs

In the spirit of a liberal arts education, we note that one need not be considering a career in physical science to find a physics, astrophysics, or astronomy major beneficial and stimulating. The physics core curriculum and the astronomy core curriculum listed below both provide excellent training in quantitative reasoning and independent problem solving, skills that are applicable in a wide variety of arenas (finance, law, medicine, science journalism, public policy). Since all of the fundamental areas are covered, the physics core curriculum is also excellent preparation for a career in a scientific field related to physics, such as engineering or teaching physics in high school. The astronomy curriculum is excellent preparation for teaching astronomy in high school, or working as a telescope operator or data analyst. These curricula are ideal for double majors.

While the physics core curriculum is adequate preparation for graduate study in physics, students considering graduate school are encouraged to take additional seminars, especially those listed below under “Enhanced Programs.” Most graduate programs in astronomy expect somewhat more physics preparation than the minimum listed in the astronomy curriculum. Those considering graduate school in astronomy are encouraged to take as much additional physics as scheduling permits, and ideally, to choose the astrophysics major listed below under “Enhanced Programs.”** Note: The Mathematics and Statistics Department offers many sets of courses covering similar material at different levels of sophistication. In each case noted, the most elementary version from each set has been listed. Students should always take the most advanced version for which they qualify, e.g. MATH 034 or 035 rather than MATH 033, if possible.*

**Physics Core Curriculum**

PHYS 005

PHYS 007, 008, 013, 015, 017, 018

PHYS 111, 112, 113, 114

PHYS 063, 081, 082†

MATH* 015, 025, 027, 033

**Astronomy Core Curriculum**

PHYS 005

PHYS 007, 008, 013, 015, ASTR 016, ASTR 061

4 Astronomy seminars (can include upper-level astronomy courses at Haverford)

MATH* 015, 025, 027, 033*Under some circumstances, PHYS 003, 004 can be substituted for PHYS 007, 008.**†Students who have taken ENGR 072 may substitute PHYS 083 instead of PHYS 081, 082.*

#### Enhanced Programs

These programs provide strong preparation for graduate study in physics, astrophysics, or astronomy.

**Physics Enhanced Curriculum**

In addition to the physics core requirements listed above, any two advanced seminars

**Astrophysics Curriculum**

PHYS 005

PHYS 007, 008, 013, 015, 017, 018, ASTR 016

Two Astronomy Seminars

PHYS 111, 112, 113, 114

MATH* 015, 025, 027, 033

**Other Requirements**

Seniors not in the Honors Program must complete a comprehensive exercise, which is intended both to encourage review and synthesis and to allow students to demonstrate mastery of fundamentals studied during all four years. In addition, all students must satisfy the College distribution requirements and the 20-course rule (except for special majors such as astrophysics or chemical physics, for whom the 20-course rule is waived).

### Course Major

A student applying to become either a physics major in the core program or an astronomy major should have completed or be completing PHYS 005 and either PHYS 004 or PHYS 008. Otherwise it will be impossible to fulfill all program requirements. To be accepted as a major, the applicant must have received grades of C+ or better in Physics, Astronomy, and Math courses.

A student applying to become a physics major in either the enhanced program in course or the Honors Program should have completed or be completing courses through PHYS 008, PHYS 013, PHYS 015, PHYS 017, PHYS 018. In addition, to be accepted into the course major, these courses must be completed with an average grade of C+ or better. To be accepted into the Honors Program with a physics major, the average grade should be a B or better. Grades in math courses should be at a similar level.

A student applying to become an astrophysics major in course or in honors should have completed or be completing PHYS 008, PHYS 013, PHYS 015, PHYS 017, PHYS 018, and ASTR 016. To be accepted into the Honors Program with an astronomy major, the applicant should have completed or be completing ASTR 016. In addition, applicants for the Honors Program in either astrophysics or astronomy must normally have an average grade in physics and astronomy courses of B or better.

Since almost all advanced work in physics and astronomy at Swarthmore is taught in seminars where the student participants share the pedagogical responsibility, an additional consideration in accepting (retaining) majors is the presumed (demonstrated) ability of the students not only to benefit from this mode of instruction but also to contribute positively to the seminars. Grades in prior courses are the best criteria in admitting majors, since they tend to indicate reliably whether or not the student can handle advanced work at Swarthmore levels without being overwhelmed. However, constructive participation in classes and laboratories is also considered.

#### Program for the Last Two Years

The following one-credit physics seminars are offered on a regular basis (regardless of faculty leaves):

Prerequisites: PHYS 005, 007, 008, 013, 015, 017, and 018

PHYS 111. Classical Mechanics

PHYS 112. Electrodynamics

PHYS 113. Quantum Theory

PHYS 114. Statistical Physics

Additional prerequisite: ASTR 016

ASTR 121. Research Techniques in Observational Astronomy (offered in alternate years)

ASTR 123. Stars and Stellar Structure (offered in alternate years)

ASTR 126. The Interstellar Medium (offered in alternate years)

In addition, one or two one-credit advanced physics seminars are offered each year. Typical topics are:

PHYS 130. General Relativity

PHYS 131. Particle Physics

PHYS 132. Non-Linear Dynamics and Chaos

PHYS 133. Atomic Physics and Spectroscopy

PHYS 134. Advanced Quantum Physics

PHYS 135. Solid State Physics

PHYS 136. Quantum Optics and Lasers

PHYS 137. Computational Physics

PHYS 138. Plasma Physics

PHYS 139. Biophysics

### Course Minor

The Physics and Astronomy Department offers two types of course minor, one in physics and one in astronomy.

#### Physics Minor Curriculum

PHYS 005

PHYS 007

PHYS 008

PHYS 013

PHYS 015

PHYS 017

PHYS 018

PHYS 111 and 113†

MATH* 015, 025, 033

*Under some circumstances, PHYS 003 and/or PHYS 004 may be substituted for PHYS 007 and/or PHYS 008.*

*†We prefer that minors have two advanced seminars, one in “classical” and one in “quantum” physics. PHYS 111 is a prerequisite for future seminars and fulfills the “classical” requirement. While we recommend PHYS 113 as the second advanced seminar, a different seminar may be substituted upon consultation with the Chair.*

### Astronomy Minor Curriculum

PHYS 005

PHYS 007 *or *PHYS 003

PHYS 008 *or *PHYS 004

ASTR 016

One Astronomy seminar numbered 100 or above

One semester of ASTR 061 (0.5 credits)

MATH* 015, 025, 033

* Note: The Mathematics and Statistics Department offers many sets of courses covering similar material at different levels of sophistication. In each case noted, the most elementary version from each set has been listed. Students should always take the most advanced version for which they qualify.

### Honors Major

Honors majors must meet the requirements for the major as described on the first page, and select** **three of the following preparations, plus their prerequisites.

#### Honors Major Programs

Physics: Electrodynamics (PHYS 112), Quantum Theory (PHYS 113), Statistical Physics (PHYS 114), Honors Thesis (PHYS/ASTR 180)

Astrophysics: Any of the seminars from the astronomy program, plus: Electrodynamics (PHYS 112), Quantum Theory (PHYS 113), Statistical Physics (PHYS 114), Honors Thesis (PHYS/ASTR 180)*Note:* must include at least one seminar each from the astronomy and physics side of the program.

Astronomy: Research Techniques in Observational Astronomy (ASTR 121), Stars and Stellar Structure (ASTR 123), The Interstellar Medium (ASTR 126), Honors Thesis (ASTR 180)*Note:* External examination for honors major programs includes two or three 3-hour written examinations on the chosen preparations, plus two or three 30-45 minute oral examinations on the chosen preparations, plus one 45-60 minute oral examination on the honors thesis (for thesis writers).

### Honors Minor

Physics: One of the following seminars PHYS 112, PHYS 113, PHYS 114

Astrophysics: One of the following seminars PHYS 112, PHYS 113, PHYS 114, ASTR 121, ASTR 123, ASTR 126

Astronomy: One of the following seminars (ASTR 121, ASTR 123, ASTR 126)*Note:* External examination for honors minor programs includes one three-hour written examination on the chosen preparations, plus one 30-45 minute oral examination on the chosen preparations.

### Research Opportunities

#### Advanced Laboratory Program

In the junior and senior years, all physics majors must take PHYS 081 and PHYS 082. Students enrolled in PHYS 081 and PHYS 082 must arrange their programs so that they can schedule an afternoon for the laboratory each week free of conflicts with other classes, typically Friday afternoon. Enrollment in each of these laboratories will appear on the student’s transcript with a letter grade for 0.5 credit for each semester. PHYS 081, 082 together count as a “writing course” for collegiate graduation requirements. Students with credit for ENGR 072 may replace PHYS 081, 082 with PHYS 083, which is an advanced lab experience without an electronics component.

#### Independent Work

Physics, astrophysics, and astronomy majors are encouraged to undertake independent research projects, especially in the senior year, either in conjunction with one of the senior seminars, or as a special project for separate credit (PHYS/ASTR 094). Members of the physics or astronomy faculty are willing to suggest possible projects and to supervise one of these if the student chooses to pursue it. Students completing work under PHYS/ASTR 094 are required to submit final written and oral reports of their work to the department. In preparation for independent experimental work, prospective physics majors are strongly urged to take the required 0.5 credit course PHYS 063, Procedures in Experimental Physics, during their fall semester of their sophomore year, which will qualify them to work in the departmental shops. There are usually many opportunities for students to receive financial support to work with faculty members on research projects during the summer.

#### Thesis

Students may do a theoretical or experimental research thesis representing the results of independent work done under the supervision of a faculty member. This thesis will usually cover work begun in the summer after the junior year and completed during the senior year. A thesis is recommended of all students in the Honors Program.

### Off-Campus Study

With proper planning, study away from Swarthmore for one or two semesters is possible while majoring in physics, astronomy, or astrophysics. However, the many prerequisites in the Physics and Astronomy Department make careful planning for study abroad a necessity. Spring of junior year is often the easiest time to make this work. The important point is to begin planning at an early stage. This allows students (1) to make sure courses not available abroad are taken at Swarthmore, and (2) to find out well in advance what physics and astronomy courses are available in the various study abroad programs. While it is completely feasible to complete a physics major without taking physics abroad (e.g. if one is studying in a non-English-speaking country), students should note when planning their programs that PHYS 111 must be taken before PHYS 113 or PHYS 114.

### Teacher Certification

We offer teacher certification in physics through a program approved by the state of Pennsylvania. For further information about the relevant set of requirements, contact the Educational Studies Department chair, the Physics Department chair, or visit the Educational Studies Department website at www.swarthmore.edu/educationalstudies.xml.

### Physics Courses

##### PHYS 002E. First-Year Seminar: Energy

This seminar will cover both the physics and policy of energy in all its forms. Topics include the physical basis for energy; thermodynamics and engines; energy sources (fossil fuels, solar, photovoltaics, nuclear); transportation; the electric grid; and climate change.

Prerequisite: High school algebra.

1 credit.

Not offered 2013–2014.

##### PHYS 002M. First-Year Seminar: Physics in Modern Medicine

The impact that physics has had on the practice of clinical medicine in the past decade has been nothing short of staggering. This seminar introduces nonscientists to the physics behind many of the diagnostic and therapeutic techniques of modern medicine as well as the basic physics behind many physiological systems in the human body. In addition to the scientific basis of the subject, covered in a modern text, the societal, ethical and economic implications will be treated through readings from other sources and through medical site visits. Topics will include: laser surgery, photodynamic therapy, ultrasound imaging, x-ray and radionuclide imaging, computer tomography (CAT or CT scans), positron emission tomography (PET scans), radiation therapy, magnetic resonance (MRI) and recent advances in optical imaging methods.

Prerequisites: None. Mathematical level: only algebra and some basic trigonometry.

1 credit.

Fall 2013. Moscatelli.

##### PHYS 003. General Physics I

Topics include vectors, kinematics, Newton’s laws and dynamics, conservation laws, work and energy, oscillatory motion, systems of particles, and rigid body rotation. Possible additional topics are special relativity and thermodynamics. Includes one laboratory weekly.

Natural sciences and engineering practicum.

Prerequisite: MATH 015 (can be taken concurrently).

1 credit.

Fall 2013. Graves.

##### PHYS 004. General Physics II

Topics include wave phenomena, geometrical and physical optics, electricity and magnetism, and direct and alternating current circuits. Possible additional topics may be added. Includes one laboratory weekly.

Natural sciences and engineering practicum.

Prerequisites: PHYS 003 or the permission of the instructor, MATH 025 (can be taken concurrently).

1 credit.

Spring 2014. Moscatelli.

##### PHYS 004L. General Physics II: Electricity, Magnetism, and Optics with Biological and Medical Applications

PHYS 004L will cover the same topics as PHYS 004 but will emphasize biological, biochemical, and medical applications of those topics. The course will meet medical school requirements (in conjunction with PHYS 003) and will include a weekly laboratory. Students who wish to take PHYS 004L before PHYS 003 must have some high school physics background and obtain permission from the instructor.

Natural sciences and engineering practicum.

Prerequisites: MATH 015 or a more advanced calculus course; PHYS 003 or permission of the instructor.

1 credit.

Spring 2014. Crouch.

##### PHYS 005. Spacetime and Quanta

This course presents an introduction to the twin pillars of contemporary physics: relativity and quantum theory. Students will explore the counterintuitive consequences of special relativity for our understanding of space and time, and the nature of the subatomic quantum world, where our notions of absolute properties such as position or speed of a particle are replaced by probabilities. It is the usual entry point to majoring or minoring in astronomy, astrophysics, or physics, and is a pre- or co-requisite for the sophomore-level physics major curriculum; it welcomes both non-majors and prospective majors who are interested in engaging rigorously and deeply with both the mathematical and conceptual descriptions of physics. Physics 005 will be taught seminar-style, with student presentation of problem solutions and ideas playing an essential role. Includes six afternoon labs and some evening telescope observing. Not eligible for NSEP credit.

1 credit.

Fall 2013. Crouch.

##### PHYS 007. Introductory Mechanics

An introduction to classical mechanics. This course is suitable for potential majors, as well as students in other sciences or engineering who would like a course with more mathematical rigor and depth than PHYS 003. Includes the study of kinematics and dynamics of point particles; conservation principles involving energy, momentum and angular momentum; rotational motion of rigid bodies, and oscillatory motion. Includes one laboratory weekly: used for hands-on experimentation and occasionally for workshops that expand on lecture material.

Natural sciences and engineering practicum.

Prerequisites: MATH 025 (can be taken concurrently), PHYS 005 or permission of the instructor.

1 credit.

Fall 2013. Mewes.

##### PHYS 008. Electricity, Magnetism, and Waves

A sophisticated introductory treatment of wave and electric and magnetic phenomena, such as oscillatory motion, forced vibrations, coupled oscillators, Fourier analysis of progressive waves, boundary effects and interference, the electrostatic field and potential, electrical work and energy, D.C. and A.C. circuits, the relativistic basis of magnetism, Maxwell’s equations, and geometrical optics. Includes one laboratory weekly.

Natural sciences and engineering practicum.

Prerequisites: PHYS 007 (or permission of instructor); MATH 033 (can be taken concurrently).

1 credit.

Spring 2014. Smith.

##### PHYS 013. Thermodynamics / Statistical Mechanics

A half-semester introductory course in thermal and statistical physics. Topics include energy, heat, work, entropy, temperature (the First, Second and “Third” Laws of Thermodynamics), heat capacity, ideal gases, paramagnetism, phase transitions, and the chemical potential. This course serves as a prerequisite for PHYS 114 and for PHYS 135. This class has a weekly laboratory requirement.

Prerequisite: single-variable calculus (MATH 025 or 026); may be taken as a corequisite with permission of the instructor.

First half of the semester.

0.5 credit.

Spring 2014. Grossman.

##### PHYS 015. Optics

A half-semester introduction to geometric and wave optics, including ray diagrams, matrix optics, polarization, Jones matrices, interference, and diffraction. This class has a weekly laboratory requirement.

Prerequisite: single-variable calculus (MATH 025 or 026); may be taken as a corequisite with permission of the instructor.

Second half of the semester.

0.5 credit.

Spring 2014. Grossman.

##### PHYS 017. Mathematical Methods of Physics

A half-semester survey of mathematical techniques useful in physics. Topics include eigenvalue problems, Fourier analysis, solutions to ordinary and partial differential equations, special functions, the theory of residues, and numerical methods. Includes a weekly numerical laboratory. Prerequisite: linear algebra (MATH 027, 028, or 028S); corequisite: multivariable calculus (MATH 033, 034, or 035).

First half of the semester.

0.5 credit.

Spring 2014. Mewes.

##### PHYS 018. Quantum Mechanics

A half-semester introductory course in quantum mechanics. Topics include waves, photons, the Schrodinger equation, Dirac notation, one-dimensional potentials, quantized angular momentum, and central potentials. This course serves as a prerequisite for PHYS 113. This class has a weekly laboratory requirement.

Prerequisites: PHYS 005, PHYS 017; corequisite: multivariable calculus (MATH 033, 034, or 035).

Second half of the semester.

0.5 credit.

Spring 2014. Mewes.

##### PHYS 020. Principles of the Earth Sciences

An analysis of the forces shaping our physical environment, drawing on the fields of geology, geophysics, meteorology, and oceanography. Includes some laboratory and fieldwork.

Natural sciences and engineering practicum.

1 credit.

Not offered 2013–2014.

##### PHYS 021. Light and Color

The fundamentals of light from the classical and quantum physical viewpoint. Extensive use of examples from art, nature, and technology will be made. Two or three lectures per week plus a special project/laboratory.

1 credit.

Not offered 2013–2014.

##### PHYS 022. Physics of Musical Sounds

An introduction to the science and technology of musical sounds and the instruments that make them. Particular attention is paid to electronic music and instruments. Topics include complex waveforms, scales and temperament, basic electronic sound devices, and digital sound technology. The course has a weekly laboratory requirement.

1 credit.

Not offered 2013–2014.

##### PHYS 024. The Earth’s Climate and Global Warming

A study of the complex interplay of factors influencing conditions on the surface of the Earth. Basic concepts from geology, oceanography, and atmospheric science lead to an examination of how the Earth’s climate has varied in the past, what changes are occurring now, and what the future may hold. Besides environmental effects, the economic, political, and ethical implications of global warming are explored, including possible ways to reduce climate change. Includes one laboratory every other week.

Natural sciences and engineering practicum.

1 credit.

Spring 2014. Collings.

##### PHYS 027. The Dark Universe

This course introduces non-science students to our modern understanding of cosmology. In the short span of 40 years, modern cosmology has transformed from a purely theoretical field to one overflowing with increasingly precise data. As a result, our picture of how the universe came into being and how it evolves in time has come into near-perfect focus: it seems as though, after thousands of years of thought, we may be on the cusp of understanding the physical nature of our ultimate origin. Although correct in certain respects, this sense of understanding may not be as founded as we might hope. We will critically explore the theoretical motivation and observational evidence that supports our modern cosmological model. We will also discuss the social and philosophical implications of humanity's attempts to understand and order the cosmos.

1 credit

Offered Spring 2014. Smith.

##### PHYS 029. Seminar on Gender and (Physical) Science

This seminar will take a multifaceted approach to the question: “What are the connections between a person’s gender, race, or class and their practice of science?” The history of science, the education of women and feminist pedagogy, and philosophy of science will be addressed. Physical science will be the principal focus. Includes some laboratory work.

Eligible for GSST credit.

1 credit.

Not offered 2013–2014.

##### PHYS 093. Directed Reading

This course provides an opportunity for an individual student to do special study, with either theoretical or experimental emphasis, in fields not covered by the regular courses and seminars. The student will present oral and written reports to the instructor.

0.5, 1, or 2 credits.

Each semester. Staff.

##### PHYS 094. Research Project

Initiative for a research project may come from the student, or the work may involve collaboration with ongoing faculty research. The student will present a written and an oral report to the department.

0.5, 1, or 2 credits.

Each semester. Staff.

### Physics Advanced Seminars

##### PHYS 111. Analytical Dynamics

Intermediate classical mechanics. Motion of a particle in one, two, and three dimensions; Kepler’s laws and planetary motion; phase space; oscillatory motion; Lagrange equations and variational principles; systems of particles; collisions and cross sections; motion of a rigid body; Euler’s equations; rotating frames of reference; small oscillations; normal modes; and wave phenomena.

Prerequisites: PHYS 005, 007, 008, and 017.

1 credit.

Fall 2013. Collings.

##### PHYS 112. Electrodynamics

Electricity and magnetism using vector calculus, electric and magnetic fields, dielectric and magnetic materials, electromagnetic induction, Maxwell’s field equations in differential form, displacement current, Poynting theorem and electromagnetic waves, boundary-value problems, radiation and four-vector formulation of relativistic electrodynamics.

Prerequisites: PHYS 111.

1 credit.

Fall 2013. Smith.

##### PHYS 113. Quantum Theory

Postulates of quantum mechanics, operators, eigenfunctions, and eigenvalues, function spaces and hermitian operators; bra-ket notation, superposition and observables, fermions and bosons, time development, conservation theorems, and parity; angular momentum, three-dimensional systems, matrix mechanics and spin, coupled angular momenta, time-independent and time-dependent perturbation theory.

Prerequisites: PHYS 018, 111; PHYS 112 strongly recommended.

1 credit.

Spring 2014. Mewes.

##### PHYS 114. Statistical Physics

The statistical behavior of classical and quantum systems; temperature and entropy; equations of state; engines and refrigerators; statistical basis of thermodynamics; microcanonical, canonical, and grand canonical distributions; phase transitions; statistics of bosons and fermions; black body radiation; electronic and thermal properties of quantum liquids and solids.

Prerequisites: PHYS 013, 111.

1 credit.

Spring 2014. Graves.

##### PHYS 115. Modern and Quantum Optics

A modern treatment of matrix optics, interference, polarization, diffraction, Fourier optics, coherence, Gaussian beams, resonant cavities, optical instruments. The quantization of the electromagnectic field, single mode coherent and quadrature squeezed states. The interaction of light with atoms using second quantization and dressed states. Spontaneous emission.

Prerequisites: PHYS 015, 111, 112 (or concurrently with instructor’s permission), and 113.1 credit.

Not offered 2013–2014.

##### PHYS 130. General Relativity

Newton’s gravitational theory, special relativity, linear field theory, gravitational waves, measurement of space-time, Riemannian geometry, geometrodynamics and Einstein’s equations, the Schwarzschild solution, black holes and gravitational collapse, and cosmology.

Prerequisites: PHYS 111 and 112.

1 credit.

Not offered 2013–2014.

##### PHYS 131. Particle Physics

A study of the ultimate constituents of matter and the nature of the interactions between them. Topics include relativistic wave equations, symmetries and group theory, Feynman calculus, quantum electrodynamics, quarks, gluons, and quantum chromodynamics, weak interactions, gauge theories, the Higgs particle, and some of the ideas behind lattice gauge calculations.

Prerequisites: PHYS 113 (may be taken concurrently).

1 credit.

Not offered 2013–2014.

##### PHYS 132. Nonlinear Dynamics and Chaos

Nonlinear mappings, stability, bifurcations and catastrophe, conservative and dissipative systems, fractals, and self-similarity in chaos theory.

Prerequisite: PHYS 111.

1 credit.

Not offered 2013–2014.

##### PHYS 135. Solid-State Physics

Crystal structure and diffraction, the reciprocal lattice and Brillouin zones, lattice vibrations and normal modes, phonon dispersion, Einstein and Debye models for specific heat, free electrons and the Fermi surface, electrons in periodic structures, the Bloch Theorem, band structure, semiclassical electron dynamics, semiconductors, magnetic and optical properties of solids, and superconductivity.

Prerequisites: PHYS 113 and PHYS 114.

1 credit.

Not offered 2013–2014.

##### PHYS 136. Quantum Optics and Lasers

Atom-field interactions, stimulated emission, cavities, transverse and longitudinal mode structure, gain and gain saturation, nonlinear effects, coherent transients and squeezed states, pulsed lasers, and super-radiance.

Prerequisite: PHYS 113.

1 credit.

Not offered 2013–2014.

##### PHYS 137. Computational Physics

Along with theory and experiment, computation is a third way to understand physics and do research. We will study concepts of scientific computing and apply these within techniques like Monte Carlo, Molecular Dynamics, Finite-Difference, and Fourier Transform methods. We will explore object-oriented strategies for scientific problem solving. Simulations relevant to classical mechanics, electromagnetism, quantum mechanics, and statistical physics will be written. Students will do an independent project of their choice.

Prerequisites: PHYS 111 and, taken previously or concurrently, PHYS 113 and 114, or special permission of the instructor.

1 credit.

Not offered 2013–2014.

##### PHYS 138. Plasma Physics

An introduction to the principles of plasma physics. Treatment will include the kinetic approach (orbits of charged particles in electric and magnetic fields, statistical mechanics of charged particles) and the fluid approach (single fluid magnetohydrodynamics, two fluid theory). Topics may include transport processes in plasmas (conductivity and diffusion), waves and oscillations, controlled nuclear fusion, and plasma astrophysics.

Prerequisite: PHYS 112.

1 credit.

Not offered 2013–2014.

##### PHYS 180. Honors Thesis

Theoretical or experiment work culminating in a written honors thesis. Also includes an oral presentation to the department. This course must be completed by the end of, and is normally taken in, the fall semester of the student’s final year.

1 or 2 credits.

Each semester. Staff.

### Physics Laboratory Program

##### PHYS 063. Procedures in Experimental Physics

Techniques, materials, and the design of experimental apparatus; shop practice; printed circuit design and construction. This is a 0.5-credit course open only to majors in physics, astrophysics, or astronomy.

0.5 credit.

Fall 2013. Technical staff.

##### PHYS 081. Advanced Laboratory I

This is the first of a two-semester sequence designed to fulfill the physics major advanced laboratory requirement. Students will perform projects in digital electronics. They will also perform experiments chosen from among the areas of thermal and statistical physics, solid state, atomic, plasma, nuclear, biophysics, condensed matter physics, and advanced optics.

Writing course.

0.5 credit.

Each semester. Staff.

##### PHYS 082. Advanced Laboratory II

This is the second of a two-semester sequence designed to fulfill the physics major advanced laboratory requirement. Students will perform projects in digital electronics. They will also perform experiments chosen from among the areas of thermal and statistical physics, solid state, atomic, plasma, nuclear, biophysics, condensed matter physics, and advanced optics. When both PHYS 081 and 082 are taken, students will receive credit for having completed a writing (W) course.

Writing course.

0.5 credit.

Each semester. Staff.

##### PHYS 083. Advanced Laboratory I and II

This course is designed to fulfill the physics major advanced laboratory requirement for students who have already had sufficient experience with digital electronics (ENGR 072 or the equivalent). Students will perform experiments chosen from among the areas of thermal and statistical physics, solid state, atomic, plasma, nuclear, biophysics, condensed matter physics, and advanced optics.

Writing course.

0.5 credit.

Each semester. Staff.

### Astronomy Courses

##### ASTR 001. Introductory Astronomy

The scientific investigation of the universe by observation and theory, including the basic notions of physics as needed in astronomical applications. Topics may include the appearance and motions of the sky; history of astronomy; astronomical instruments and radiation; the sun and planets; properties, structure, and evolution of stars; the galaxy and extragalactic systems; the origin and evolution of the universe; and prospects for life beyond Earth. Includes six evening labs.

Natural sciences and engineering practicum.

1 credit.

Spring 2014. Cohen.

##### ASTR 006. Introductory Cosmology

A half-semester introductory course on cosmology, with an emphasis on the basics of standard Big Bang cosmology, its theoretical framework, and its observational underpinnings. Topics covered will include a qualitative treatment of general relativity, a Newtonian derivation of the Friedmann equation and associated solutions for model universes, the expansion of the Universe, the cosmic microwave background, and big-bang nucleosynthesis. We also will explore more recent observational measurements of the properties of dark matter and dark energy as well as the growth of structure in the Universe. This course is intended for first-year students who are considering physics, astrophysics, or astronomy majors but it is suitable for other students with similar backgrounds and interests as well.

Prerequisites: Math 25 or equivalent being taken at least concurrently; some classical physics, at least at the high school level. No astronomy background is presumed.

Second half of semester.

0.5 credit.

Fall 2013. Cohen.

##### ASTR 016. Modern Astrophysics

This is a one-semester calculus- and physics-based introduction to astrophysics as applied to stars, the interstellar medium, galaxies, and the large-scale structure of the universe. The course includes four evening laboratories and observing sessions.

Prerequisites: MATH 015 and 025, and some prior work in calculus-based physics (which could include high school physics). *Recommended* (but not required) pre- or co-requisites are PHYS 013; PHYS 015; and/or PHYS 007 or PHYS 003. Interested students should consult with the instructor.

1 credit.

Fall 2013. Cohen.

##### ASTR 020. Black Holes and The Big Bang

This course introduces non-science students to our current understanding of black holes, the Big Bang, and the fate of the universe. Students will learn what black holes are, how they are formed, what strange effects they have on space and time, and what happens when something falls into a black hole. We will discuss observational evidence of black holes and techniques for detecting small miniature black holes as well as monstrous supermassive ones that lurk in the centers of galaxies. We will also cover concepts of general relativity, the history of the universe, acceleration of its expansion and dark energy.

Prerequisites: High school level algebra.

1 credit.

Not offered 2013–2014.

##### ASTR 061. Current Problems in Astronomy and Astrophysics

Reading and discussion of selected research papers from the astronomical literature. Techniques of journal reading, use of abstract services, and other aids for the efficient maintenance of awareness in a technical field. May be repeated for credit. Credit/No Credit only.Prerequisite: ASTR 016.

0.5 credit.

Spring 2014. Cohen, Jensen.

##### ASTR 093. Directed Reading

(See PHYS 093)

##### ASTR 094. Research Project

(See PHYS 094)

### Astronomy Seminars

*Students interested in upper-level work in astronomy are encouraged to also consult Haverford’s course schedule, since the two astronomy programs actively work to offer complementary topics.*

##### ASTR 121. Research Techniques in Observational Astronomy

This course covers many of the research tools used by astronomers. These include instruments used to observe at wavelengths across the electromagnetic spectrum; techniques for photometry, spectroscopy, and interferometry; and various methods by which images are processed and data are analyzed; and use of online resources including data archives and bibliographic databases. Students will perform observational and data analysis projects during the semester, culminating in a group research paper using new data to address an open scientific question.

Prerequisite: PHYS 015; ASTR 016.

1 credit.

Spring 2014. Jensen.

##### ASTR 123. Stellar Astrophysics

An overview of physics of the stars, both atmospheres and interiors. Topics may include hydrostatic and thermal equilibrium, radiative and convective transfer nuclear energy generation, degenerate matter, calculation of stellar models, interpretation of spectra, stellar evolution, white dwarfs and neutron stars, nucleosynthesis, supernovae, and star formation.

Prerequisites: PHYS 013; ASTR 016. PHYS 017 and 018 recommended.

1 credit.

Not offered 2013–2014.

##### ASTR 125. Stars in the Interstellar Medium

An overview of physics of the stars with related interstellar medium topics. Topics may include hydrostatic and thermal equilibrium, energy transport, nuclear energy generation, degenerate matter and compact

objects, interpretation of spectra, stellar evolution, nucleosynthesis, and – transitioning to the interstellar medium topics –supernovae, star formation, cooling mechanisms, emission nebulae, absorption spectroscopy of interstellar clouds, hydrodynamics and shock waves, interstellar molecules, and dust.

Prerequisites: PHYS 013; ASTR 016. PHYS 017 and 018 recommended.

1 credit.

Spring 2015. Cohen.

##### ASTR 126. The Interstellar Medium

Study of the material between the stars and radiative processes in space, including both observational and theoretical perspectives on heating and cooling mechanisms, physics of interstellar dust, chemistry of interstellar molecules, magnetic fields, emission nebulae, hydrodynamics and shock waves, supernova remnants, star-forming regions, the multiphase picture of the interstellar medium.

Prerequisites: PHYS 013; ASTR 016. PHYS 017 and 018 recommended.

1 credit.

Not offered 2013–2014.

##### ASTR 129. Cosmology

Cosmology is the study of the overall structure, history, and future evolution of the universe. This seminar will cover the following topics: the distance ladder; Hubble’s law; Einstein’s general theory of relativity; Friedmann models of the Universe; high-redshift supernovae; the cosmic microwave background; dark matter and dark energy; the early universe including big bang nucleosynthesis and inflation; the age of the universe and the “Cosmic Concordance.”

Natural sciences and engineering practicum.

Prerequisites: Prerequisites: ASTR 016 or PHYS 013 and PHYS 017

1 credit.

Fall 2014. Cohen

##### ASTR 180. Honors Thesis

(See PHYS 180)

1 or 2 credits.

Each semester. Staff.