Students may complete a major or minor in Physics. Within the major, students may complete a minor in educational studies or complete the requirements for secondary education certification. Students may complete an M.A. in the combined A.B./M.A. program.

Peter A. Beckmann, Professor and Chair

Xuemei Cheng, Assistant Professor

Daniel Cross, Lecturer

Mark Matlin, Senior Lecturer

Elizabeth McCormack, Dean of Graduate Studies and Professor

Michael Noel, Associate Professor (on leave semester I)

Michael B. Schulz, Assistant Professor (on leave semesters I and II)

Stephanie Lim, Bucher-Jackson Postdoctoral Fellow

The courses in Physics emphasize the concepts and techniques that have led to our present way of modeling the physical world around us. They are designed both to relate the individual parts of physics to the whole and to treat the various subjects in depth. Opportunities exist for interdisciplinary work and for participation by qualified majors in research with members of the faculty and their graduate students. In addition, qualified seniors may take graduate courses.

The introductory courses required for the physics major and minor are PHYS 121 and PHYS 122 (or PHYS 101 and 102) and MATH 101 and MATH 102. Although College credit is given for a score of 4 or 5 on the AP tests and for a score of 5 or above on the IB examination, the AP and IB courses are not equivalent to PHYS 121 and PHYS 122 and advanced placement will not, in general, be given. However, students with a particularly strong background in physics are encouraged to take the departmental advanced placement examination either during the summer before entering Bryn Mawr or just prior to, or during, the first week of classes. Then, the department can place students in the appropriate course. Students are not given credit for courses they place out of as a result of taking this placement exam. It is best for a student considering a physics major to complete the introductory requirements in the first year. However, the major sequence is designed so that a student who completes the introductory sequence by the end of the sophomore year can major in physics.

**Major Requirements**

Beyond the two introductory physics courses and the two introductory mathematics courses, nine additional courses are required for the major. (Haverford courses may be substituted for Bryn Mawr courses where appropriate.) Six of the nine courses must be PHYS 201, 214, 306, 331, and MATH 201, 203. The remaining three courses must be chosen from among the other 300-level physics courses, one of which may be substituted with any one course from among ASTR 320, 321, and 333, or any 300-level math course.

The department has been very successful in preparing students for graduate school in physics, physical chemistry, materials science, engineering, and related fields. To be well prepared for graduate school, students should take, at a minimum, PHYS 302, 303, 308, and 309 (in addition to PHYS 306 and 331 which are required for the major). PHYS 322 AND PHYS 325 also are highly recommended. These students should also take any additional physics, mathematics, and chemistry courses that reflect their interests, and should engage in research with a member of the faculty by taking PHYS 403. (Note that PHYS 403 is usually two semesters and does not count towards the 13 courses required for the major.) Seniors can take graduate courses, usually PHYS 501: Quantum Mechanics or PHYS 503: Electromagnetism, to get a head start on graduate school.

Typical plans for a basic four-year major in physics are listed below.

**Four-Year Plan meeting the minimum requirements for the major:**

**1st Year**

PHYS 121, 122

MATH 101, 102

**2nd Year**

PHYS 201, 214

MATH 201, 203

**3rd Year**

PHYS 306, 331, and one other 300-level physics course

**4th Year**

Two 300-level physics courses

**Four-Year Plan providing a minimum preparation for graduate school:**

**1st Year**

PHYS 121, 122

MATH 101, 102

**2nd Year**

PHYS 201, 214

MATH 201, 203

**3rd Year**

PHYS 306, 331, and either 303, 309 or 308, 302

**4th Year**

PHYS 308, 302 or 303, 309

PHYS 403 (both semesters)

The physics program at Bryn Mawr allows for a student to major in physics even if the introductory courses are not completed until the end of the sophomore year, as long as calculus (MATH 101 and 102) is taken in the first year. It is also possible for the student majoring in three years to be adequately prepared for graduate school. To do this, the outline below should be supplemented with (at least) PHYS 403 for both semesters in the 4th year.

**Three-Year Plan meeting the minimum requirements for the major:**

**1st Year**

MATH 101, 102

**2nd Year **

PHYS 121, 122

MATH 201, 203

**3rd Year**

PHYS 201, 214, 306, 331

**4th Year**

Three 300-level physics courses

**Honors**

The degree of Bachelor of Arts is awarded with honors in physics in recognition of academic excellence. The award, which is made upon the recommendation of the department, is based on the quality of a Senior Thesis and on an achievement of a GPA of at least 3.4 in 200-level courses and above in physics, astronomy, and mathematics at Bryn Mawr and Haverford Colleges and an overall GPA of at least 3.0.

**Minor Requirements**

The requirements for the minor, beyond the introductory sequence, are PHYS 201, 214, 306, 331; MATH 201, 203; and one additional 300-level physics course. The astronomy and mathematics courses described under “Major Requirements” may not be substituted for the one additional 300-level physics course.

**Minor in Educational Studies or
Secondary-School Teacher Certification**

Students majoring in physics can pursue a minor in educational studies or state certification to teach at the secondary-school level. Students seeking the minor need to complete six education courses including a two-semester senior seminar, which requires five to eight hours per week of fieldwork. To earn secondary-school certification (grades 7-12) in physics, students must: complete the physics major plus two semesters of chemistry and one semester as a teaching assistant in a laboratory for introductory or intermediate physics courses; complete six education courses; and student-teach full-time (for two course credits) second semester of their senior year.

**A.B./M.A. Program**

To earn an M.A. degree in physics in the College’s A.B./M.A. program, a student must complete the requirements for an undergraduate physics major and also must complete six units of graduate level work in physics. Of these six units, as many as two units may be undergraduate courses at the 300 level taken for graduate credit (these same two courses may be used to fulfill the major requirements for the A.B. degree), at least two units must be graduate seminars at the 500 level, and two units must be graduate research at the 700 level leading to the submission and oral defense of an acceptable M.A. thesis.

3-2 Program in Engineering
and Applied Science

The 3-2 Program in Engineering and Applied Science is offered in cooperation with the California Institute of Technology. Students spend three years at Bryn Mawr, during which time they must complete all non-major requirements. Students then apply to Caltech as a transfer student and admission is determined by Caltech. Students earn both an A.B. at Bryn Mawr and a B.S. at Caltech. Financial aid is not available at Caltech for non-US citizens.

**Courses at Haverford College**

Many upper-level physics courses are taught at Haverford and Bryn Mawr in alternate years as indicated in the listings of the specific courses below. These courses (numbered 302, 303, 308, 309, and 322) may be taken at either institution to satisfy major requirements. In addition, 100- and 200-level courses can be used to replace 100- and 200-level courses at Bryn Mawr but these courses are not identical and careful planning is required.

**Introductory Physics Sequences**

Students on a pre-health professions track wanting to take one year of physics should take PHYS 101 and PHYS 102. Some students on a physical sciences major track could take PHYS 121 and PHYS 122 and others might take PHYS 122 and PHYS 201. See your major adviser and carefully note the math pre- and co-requisites for these courses. PHYS121/122/201/214 is a coordinated, four-semester sequence in physics.

**PHYS B101 Introductory Physics **

PHYS 101/102 is an introductory sequence intended primarily for students on the pre-health professions track. Emphasis is on developing an understanding of how we study the universe, the ideas that have arisen from that study, and on problem solving. Topics are taken from among Newtonian kinematics and dynamics, relativity, gravitation, fluid mechanics, waves and sound, electricity and magnetism, electrical circuits, light and optics, quantum mechanics, atomic and nuclear physics, and particle physics and cosmology. An effective and usable understanding of algebra and trigonometry is assumed. First year students who will take or place out of MATH 101 should take PHYS 121. Lecture three hours, laboratory three hours.

(Staff, Division II with Lab and Quantitative Skills)

**PHYS B102 Introductory Physics **

PHYS 101/102 is an introductory sequence intended primarily for students on the pre-health professions track. Emphasis is on developing an understanding of how we study the universe, the ideas that have arisen from that study, and on problem solving. Topics are taken from among Newtonian kinematics and dynamics, relativity, gravitation, fluid mechanics, waves and sound, electricity and magnetism, electrical circuits, light and optics, quantum mechanics, atomic and nuclear physics, and particle physics and cosmology. An effective and usable understanding of algebra and trigonometry is assumed. First year students who will take or place out of MATH 101 should take PHYS 121. Lecture three hours, laboratory three hours.

(Staff, Division II with Lab and Quantitative Skills)

**PHYS B107 Physics, Evolution, and Literature: Humans Modeling Their World**

This course addresses how human beings model physical systems far from the everyday realm, as well as how human senses work and the role of biological evolution. We develop models for electromagnetism, quantum mechanics, special relativity, general relativity, cosmology, particle physics, and nuclear physics. No mathematics is used. Readings include Abbott’s *Flatland*, Wells’ *The Country of the Blind*, Borges’ *Library of Babel*, Kafka’s *Metamorphosis*, other short stories, and selected scientific articles. Lecture three hours, discussion session one hour, laboratory three hours. This course does not satisfy the Quantitative Skills requirement. Also see PHYS 150 which is PHYS 107 without the laboratory.

(Beckmann, Division II with Lab)

*Not offered in 2010-11.*

**PHYS B108 Contemporary Physics **

The 20th century brought two revolutions in our understanding of the universe—the theories of relativity and quantum physics. We will investigate each of them and their consequences, and touch on new theories that might unify them. We will also explore “chaos theory” which applies to phenomena ranging from electrical activity in the brain during seizures to the stability of solar systems. Lecture 3 hours; Laboratory 3 hours. This course does not satisfy the Quantitative Skills requirement. Also see PHYS B158 for the lecture only course.

(Matlin, Division II with Lab)

*Not offered in 2010-11.*

**PHYS B109 How Things Work **

This course gives students the opportunity to explore the physical principles that govern the objects and activities familiar in their everyday lives. For example, objects such a roller coasters, rockets, light bulbs and Xerographic copiers will be used to explore motion, fluids, heat, and electricity. Lecture three hours, laboratory three hours. Note: this course does not satisfy the Quantitative Skills requirement. Also: see PHYS 160 which is PHYS 109 without the laboratory.

(Noel, Division II with Lab)

*Not offered in 2010-11.*

**PHYS B121 Modeling the Physical World: Foundations and Frontiers **

This course presents current conceptual understandings and mathematical formulations of fundamental ideas used in physics. Students will develop physical intuition and problem-solving skills by exploring key concepts in physics such as the conservation of energy and momentum and modern topics in physics including the unification of the fundamental forces, relativistic space-time, nuclear and particle physics, and cosmology. This course can serve as a stand-alone survey of physics or as the first of a four-semester sequence designed for those majoring in the physical sciences. Lecture three hours, laboratory three hours. Corequisite: MATH 101.

(Staff, Division II with Lab and Quantitative Skills)

**PHYS B122 Classical Mechanics **

The lecture material covers Newtonian mechanics of single particles, systems of particles, rigid bodies, and continuous media with applications, one-dimensional systems including forced and nonlinear oscillators, scattering and orbit problems. Lecture three hours, laboratory three hours. Prerequisites: PHYS 121 and MATH 101. Corequisite: MATH 102.

(Staff, Division II with Lab and Quantitative Skills)

**PHYS B157 Physics, Evolution, and Literature: Humans Modeling Their World **

PHYS 107 but without the laboratory.

(Beckmann, Division II: Natural Science)

*Not offered in 2010-11.*

**PHYS B158 Contemporary Physics **

PHYS 108 but without the laboratory

(Matlin, Division II: Natural Science)

*Not offered in 2010-11.*

**PHYS B159 How Things Work **

PHYS 109 but without the laboratory.

(Noel, Division II: Natural Science)

*Not offered in 2010-11.*

**PHYS B201 Electromagnetism **

The lecture and material covers electrostatics, electric currents, magnetic fields, electromagnetic induction, Maxwell’s equations, electromagnetic waves. Scalar and vector fields and vector calculus are introduced and developed as needed. The laboratory involves passive and active circuits and analog and digital electronics. Lecture three hours, laboratory three hours. Prerequisite: PHYS 102 or 122. Corequisite: MATH 201.

(Staff, Division II with Lab and Quantitative Skills)

PHYS B214 An Introduction to Quantum Mechanics

An introduction to the principles governing systems at the atomic scale and below. Topics include the experimental basis of quantum mechanics, wave-particle duality, Schrödinger’s equation and its solutions, the time dependence of quantum states, angular momentum in the microscopic world, simple atoms, and atomic nuclei. Recent developments, such as paradoxes calling attention to the counter-intuitive aspects of quantum physics, will be discussed. The laboratory involves quantum mechanics, solid state physics, and optics experiments. Lecture three hours, laboratory three hours. Prerequisite: PHYS 201, MATH 201. Corequisite: MATH 203.

(Staff, Division II with Lab and Quantitative Skills)

**PHYS B302 Advanced Quantum Mechanics and Applications**

This course presents nonrelativistic quantum mechanics, including Schrodinger’s equation, the eigenvalue problem, the measurement process, the hydrogen atom, the harmonic oscillator, angular momentum, spin, the periodic table, perturbation theory, and the relationship between quantum and Newtonian mechanics. Lecture three hours and additional recitation sessions as needed. Prerequisites: PHYS 214 and PHYS 306.

(Staff)

*Alternates between Bryn Mawr and Haverford; 2010-11 at Haverford.*

**PHYS B303 Statistical Mechanics and Thermodynamics **

This course presents the statistical description of the macroscopic states of classical and quantum systems, including conditions for equilibrium, the microcanonical, canonical, and grand canonical ensembles, and Bose-Einstein, Fermi-Dirac, and Maxwell Boltzmann statistics. The statistical basis of classical thermodynamics is investigated. Examples and applications are drawn from among solid state physics, low temperature physics, atomic and molecular physics, electromagnetic waves, and cosmology. Lecture three hours and additional recitation sessions as needed. Prerequisite: PHYS 214. Corequisite: PHYS 306.

(Staff)

*Alternates between Bryn Mawr and Haverford; 2010-11 at Bryn Mawr.*

**PHYS B306 Mathematical Methods in the Physical Sciences **

This course presents topics in applied mathematics useful to students, including physicists, engineers, physical chemists, geologists, and computer scientists studying the natural sciences. Topics are taken from Fourier series, integral transforms, advanced ordinary and partial differential equations, special functions, boundary-value problems, functions of complex variables, and numerical methods. Lecture three hours and additional recitation sessions as needed. Prerequisites: MATH 201 and 203.

(Staff)

**PHYS B308 Advanced Classical Mechanics **

This course presents kinematics and dynamics of particles and macroscopic systems using Newtonian, Lagrangian, and Hamiltonian mechanics. Topics include oscillations, normal mode analysis, inverse square laws, nonlinear dynamics, rotating rigid bodies, and motion in noninertial reference frames. Lecture three hours and additional recitation sessions as needed. Prerequisite: PHYS 214. Corequisite: PHYS 306.

(Staff)

*Alternates between Bryn Mawr and Haverford; 2010-11 at Haverford.*

**PHYS B309 Advanced Electromagnetic Theory **

This course presents electrostatics and magnetostatics, dielectrics, magnetic materials, electrodynamics, Maxwell’s equations, electromagnetic waves, and special relativity. Examples and applications are taken from superconductivity, plasma physics, and radiation theory. Lecture three hours and additional recitation sessions as needed. Prerequisites: PHYS 214 and 306.

(Staff)

*Alternates between Bryn Mawr and Haverford; 2010-11 at Bryn Mawr*.

**PHYS B322 Solid State Physics **

This course presents the physics of solids. Topics include crystal structure and diffraction, the reciprocal lattice and Brillouin zones, crystal binding, lattice vibrations and normal modes, phonon dispersion, Einstein and Debye models for the specific heat, the free electron model, the Fermi surface, electrons in periodic structures, the Bloch theorem and band structure. Additional topics are taken from semiclassical electron dynamics, semiconductors, superconductivity, 0-D (quantum dots), 1-D (quantum wires) and 2-D (graphene) structures and the microscopies used to investigate them. Lecture three hours and additional recitation sessions as needed. Prerequisites: PHYS 214 and 306.

(Staff)

*Alternates between Bryn Mawr and Haverford; 2010-11 at Bryn Mawr.*

**PHYS B325 Advanced Theoretical Physics **

This course presents one or more of several subjects, depending on instructor availability and student interest. The possible subjects are (1) special relativity, general relativity, and gravitation, (2) the standard model of particle physics, (3) particle astrophysics and cosmology, (4) relativistic quantum mechanics, (5) grand unified theories, (6) string theory, loop quantum gravity, and causal set theory. Lecture three hours and additional recitation sessions as needed. Prerequisites: PHYS 306 and 308. Corequisite: PHYS 302.

(Schulz)

*Not offered in 2010-11.*

**PHYS B331 Advanced Experimental Physics **

This laboratory course consists of set-piece experiments as well as directed experimental projects to study a variety of phenomena in atomic, molecular, optical, nuclear, and solid state physics. The experiments and projects serve as an introduction to contemporary instrumentation and the experimental techniques used in physics research laboratories in industry and in universities. Students write papers in a format appropriate for research publications and make a presentation to the department. Laboratory eight hours a week. Prerequisite: PHYS 201. Corequisite: PHYS 214.

(Staff)

**PHYS B380 Physics Pedagogy**

Students work with a faculty member as assistant teachers in a college course in physics, or as assistants to a faculty member developing new teaching materials. Students will be involved in some combination of the following: directed study of the literature on teaching and learning pedagogy, construction and design of parts of a course, and actual teaching in a lecture course or laboratory. Corequisite: PHYS 201.

(Matlin)

**PHYS B390 Independent Study **

At the discretion of the department, juniors or seniors may supplement their work in physics with the study of topics not covered in regular course offerings.

(Staff)

**PHYS B403 Supervised Research**

At the discretion of the department, juniors and seniors may supplement their work in physics with research in one of the faculty research groups. Students provide a written paper and give an oral presentation at the end of the semester or year. Students are encouraged to contact individual faculty members and the departmental Web pages for further information.

(Beckmann, Cheng, McCormack, Noel, Schulz)

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