## Course Offerings

The following courses are lectures unless otherwise indicated.

The Universe: Its Nature and History

PHYS-UA 7 Offered every year. 4 points.

Qualitative introduction to our understanding of the nature and evolution of the universe. Topics include the creation of the cosmos; its explosive evolution, present structure, and ultimate fate; the nature of stars and galaxies; the structure and evolution of our Milky Way; the birth, life, and eventual death of the solar system; our place and role in the universe; and the relationship of modern astronomical ideas to other cultural disciplines.

Origins of Astronomy

PHYS-UA 8 Identical to MEDI-UA 8. Offered every other year. 4 points.

Introduction to the historical development of astronomy, from earliest times through the Copernican revolution. Traces the changes in our perception of the heavens and the influences that led to those changes, from astrology to the discoveries of Galileo and the physics of Newton. Includes descriptive astronomy of the solar system and a trip to the Hayden Planetarium.

Sound and Music

PHYS-UA 10 Assumes high school-level mathematics background. Offered every year. 4 points.

Explores the production of musical sound and how it is perceived by us, dealing mainly with the physical basis of sound. Covers sound waves, resonance, how musical instruments produce sound, the concepts of scales and harmony, physical acoustics, physiological factors of perception, acoustics of auditoria, and sound recording and reproduction. Develops the necessary physics for the course, as needed.

General Physics I

PHYS-UA 11 Prerequisite: Calculus I (MATH-UA 121) or equivalent, or completion of the Mathematics for Economics I and II sequence (MATH-UA 211 and 212), or permission of the instructor. Lecture, laboratory, and recitation. Not open to students who have completed Physics I (PHYS-UA 91) with a grade of C- or better. Offered in the fall. 5 points.

Begins a two-semester introduction to physics intended primarily for preprofessional students and for those majoring in a science other than physics, although well-prepared students may wish to take the Physics I, II, III sequence for majors (with corequisite laboratories), below. Topics include kinematics and dynamics of particles; momentum, work, and energy; gravitation; circular, angular, and harmonic motion; mechanical and thermal properties of solids, liquids, and gases.

General Physics II

PHYS-UA 12 Prerequisite: General Physics I (PHYS-UA 11) with a grade of C- or better or permission of the department. Lecture, laboratory, and recitation. Offered in the spring. 5 points.

Continuation of General Physics I (PHYS-UA 11). Topics include electric charge, field, and potential; magnetic forces and fields; resistive, capacitive, and inductive circuits; electromagnetic induction; wave motion; electromagnetic waves; geometrical optics; interference, diffraction, and polarization of light; relativity; atomic and nuclear structure; elementary particle physics.

Observational Astronomy

PHYS-UA 13 Prerequisite: The Universe: Its Nature and History (PHYS-UA 7) or higher, or permission of the instructor for nonscience majors and minors; no prerequisite for science majors and minors or those who have satisfied the MAP Natural Science I requirement. Lecture and laboratory. Offered every year. 4 points.

Introduction to the theory and practice of technical amateur astronomy. The approach is hands-on, with weekly evening laboratory/observing sessions. Topics include astronomical coordinate systems, optics, how to use a telescope, and the phenomena that can be seen in the urban night sky. Observing sessions involve the use of eight-inch telescopes.

20th-Century Concepts of Space, Time, and Matter

PHYS-UA 20 Assumes high school-level geometry and intermediate algebra background. Not open to students who have completed Natural Science I: Einstein’s Universe (MAP-UA 204). Offered every year. 4 points.

The 20th century has been witness to two major revolutions in man’s concepts of space, time, and matter. Einstein’s special and general theories of relativity: implications of the special theory, for our understanding of the unity of space and time, and the general theory, for our understanding of the nature of gravity. Quantum mechanics: a new picture of the basic structure and interactions of atoms, molecules, and nuclei. Topics include the uncertainty principle, wave-particle duality, and the continuing search for the fundamental constituents of matter.

Introductory Experimental Physics I

PHYS-UA 71 Typically taken with Physics I (PHYS-UA 91). Offered in the fall. 2 points.

The first of two introductory-level laboratory courses. Introduces essential experimental techniques, including setup and operation of basic laboratory equipment, elementary experimental design, statistics and inference, and computational data analysis. Experimental techniques are introduced in the context of classic physics experiments.

Introductory Experimental Physics II

PHYS-UA 72 Prerequisite: Introductory Experimental Physics I (PHYS-UA 71). Typically taken with Physics II (PHYS-UA 93). Offered in the spring. 2 points.

Continuation of Introductory Experimental Physics I (PHYS-UA 71).

Intermediate Experimental Physics I

PHYS-UA 73 Prerequisite: Introductory Experimental Physics II (PHYS-UA 72). Typically taken with Physics III (PHYS-UA 95). Offered in the fall. 2 points.

The first of two intermediate-level laboratory courses. Develops further the experimental techniques introduced in Introductory Experimental Physics I, II (PHYS-UA 71, 72) in the context of more advanced experiments.

Intermediate Experimental Physics II

PHYS-UA 74 Prerequisite: Intermediate Experimental Physics I (PHYS-UA 73). Typically taken with Classical and Quantum Waves (PHYS-UA 105). Offered in the spring. 2 points.

Continuation of Intermediate Experimental Physics I (PHYS-UA 73).

Physics I

PHYS-UA 91 Corequisite: Calculus I (MATH-UA 121) or Honors Calculus I: Accelerated Calculus with Linear Algebra I (MATH-UA 221). Physics majors must also register for Introductory Experimental Physics I (PHYS-UA 71). Lecture and recitation. Offered in the fall. 3 points.

With PHYS-UA 93 and PHYS-UA 95, forms a three-semester sequence that must be taken in order, starting in the fall semester. Intended for physics majors and other interested science and mathematics majors. Topics include kinematics and dynamics of particles; energy and momentum; rotational kinematics and dynamics; harmonic oscillators; gravitational fields and potentials; special relativity.

Physics II

PHYS-UA 93 Prerequisite: Physics I (PHYS-UA 91) with a grade of C or better, or permission of the department. Corequisite: Calculus II (MATH-UA 122) or Honors Calculus II: Accelerated Calculus with Linear Algebra II (MATH-UA 222). Physics majors must also register for Introductory Experimental Physics II (PHYS-UA 72). Lecture and recitation. Offered in the spring. 3 points.

Continuation of Physics I (PHYS-UA 91). Topics include electrostatics; dielectrics; currents and circuits; the magnetic field and magnetic materials; induction; AC circuits; Maxwell’s equations.

Physics III

PHYS-UA 95 Prerequisite: Physics II (PHYS-UA 93) with a grade of C or better, or permission of the department. Corequisite: Calculus III (MATH-UA 123) or Honors Calculus II: Accelerated Calculus with Linear Algebra II (MATH-UA 222). Physics majors must also register for Intermediate Experimental Physics I (PHYS-UA 73). Lecture and recitation. Offered in the fall. 3 points.

Continuation of Physics II (PHYS-UA 93). Topics include wave motion; Fourier series; sound; the reflection, refraction, interference, and diffraction of light; polarization; thermodynamics; kinetic theory and statistical physics.

Classical and Quantum Waves

PHYS-UA 105 Prerequisite: Physics III (PHYS-UA 95), and either Calculus III (MATH-UA 123) or Honors Calculus II: Accelerated Calculus with Linear Algebra II (MATH-UA 222). Physics majors must also register for Intermediate Experimental Physics II (PHYS-UA 74). Lecture and recitation. Offered in the spring. 3 points.

Topics include linear and nonlinear oscillators, resonance, coupled oscillators, normal modes, mechanical waves, light, matter waves, Fourier analysis, Fourier optics (diffraction), and an introduction to numerical (computer) methods for solving differential equations.

Mathematical Physics

PHYS-UA 106 Prerequisite: Physics III (PHYS-UA 95). Lecture and recitation. Offered in the spring. 3 points.

Mathematical preparation for the junior and senior courses in physics. Vector analysis, Fourier series and integrals, ordinary differential equations, matrices, partial differential equations, and boundary-value problems.

Electronics for Scientists

PHYS-UA 110 Identical to BIOL-UA 110, CHEM-UA 671. Prerequisite: General Physics II (PHYS-UA 12) or Physics II (PHYS-UA 93) or permission of the instructor. Lecture and laboratory. Offered in the fall. 5 points.

Introduction to basic analog and digital electronics used in modern experiments and computers, for students from any science discipline. Basic concepts and devices presented in lecture are studied in the laboratory. Topics include filters, power supplies, transistors, operational amplifiers, digital logic gates, and both combinatorial and sequential digital circuits. Students learn the functions of modern electronic instrumentation and measurement.

Advanced Experimental Physics

PHYS-UA 112 Prerequisites: Intermediate Experimental Physics I, II (PHYS-UA 73, 74) and Quantum Mechanics I (PHYS-UA 123), or permission of the instructor. Laboratory. Offered every year. 3 points.

Introduces the experiments and techniques of modern physics. Students choose their experiments and may use microcomputers for data analysis. Experimental areas include optical spectroscopy, the Mössbauer effect, cosmic rays, magnetic resonance, condensed matter, and relativistic mass.

Dynamics

PHYS-UA 120 Prerequisites: Physics III (PHYS-UA 95) and Mathematical Physics (PHYS-UA 106). Offered every year. 3 points.

Intermediate-level course on the principles and applications of dynamics. Emphasis on the formulation of problems and their numerical solution. Topics include conservation laws, central force motion, Lagrange’s and Hamilton’s equations, normal modes and small oscillations, and accelerated reference frames.

Quantum Mechanics I

PHYS-UA 123 Prerequisite: Classical and Quantum Waves (PHYS-UA 105). Offered every year. 3 points.

Introduction to the experimental basis and formal mathematical structure of quantum mechanics. Topics include foundational experiments, wave-particle duality, wave functions, the uncertainty principle, the time-independent Schrödinger equation and its applications to one-dimensional problems and the hydrogen atom, angular momentum, and spin; Hilbert Space, operators, and observables; time-independent perturbation theory; atomic spectra.

Quantum Mechanics II

PHYS-UA 124 Prerequisite: Quantum Mechanics I (PHYS-UA 123). Offered every year. 3 points.

Continuation of Quantum Mechanics I (PHYS-UA 123). Topics include the time-dependent Schrödinger equation, the Schrödinger and Heisenberg description of quantum systems, time-dependent perturbation theory, scattering theory, quantum statistics, and applications to atomic, molecular, nuclear, and elementary particle physics.

Electricity and Magnetism I

PHYS-UA 131 Prerequisites: Classical and Quantum Waves (PHYS-UA 105) and Mathematical Physics (PHYS-UA 106). Offered every year. 3 points.

Introduction to electrodynamics with applications to physical problems. Topics include electrostatics, magnetostatics, Maxwell’s equations, electromagnetic forces, electromagnetic waves, radiation from accelerating charges and currents, and special relativity.

Electricity and Magnetism II

PHYS-UA 132 Prerequisite: Electricity and Magnetism I (PHYS-UA 131). Offered every year. 3 points.

Continuation of Electricity and Magnetism I (PHYS-UA 131), with greater depth and emphasis on more complex phenomena and applications. Topics include solutions to the Laplace and Poisson equations, dielectrics and magnetic materials, gauge invariance, plasmas, Fresnel equations, transmission lines, wave guides, and antennas.

Optics

PHYS-UA 133 Prerequisite: Classical and Quantum Waves (PHYS-UA 105) or permission of the instructor. 3 points.

Introduction to physical and geometrical optics. Wave phenomena including diffraction, interference, first-order and higher-order coherence. Holography, phase contrast and atomic force microscopy, and limits of resolution are some of the subjects included. Topics include atomic energy levels and radiative transitions, and detectors from photon counting to bolometers for infrared radiation.

Condensed Matter Physics

PHYS-UA 135 Prerequisite: Classical and Quantum Waves (PHYS-UA 105) or permission of the instructor. Offered every other year. 3 points.

Designed as an introduction to condensed matter physics for students with knowledge of elementary quantum mechanics. Topics include crystal structure, lattice vibrations, and the energy band theory of metals and semiconductors; the electronic, magnetic, and optical properties of solids; and some modern research topics, such as the physics of nano-structures, soft condensed matter physics, and superconductivity.

Readings in Particle Physics

PHYS-UA 136 Prerequisite: Classical and Quantum Waves (PHYS-UA 105). Offered every other year. 3 points.

Particle physics is the study of the very fundamental constituents of matter and of the forces between them. By its nature it is microscopic, but it also connects with astrophysics and cosmology on the largest scales. This course introduces the most important advances in elementary particle physics. It centers on journal articles in which these advances were first published, with overview lectures, original reading, discussion, and student presentations. Topics include the discovery of elementary particles in cosmic rays, antimatter, symmetries found in nature, and the invention of the Quark model of elementary particles and its experimental verification.

Thermal and Statistical Physics

PHYS-UA 140 Prerequisites: Classical and Quantum Waves (PHYS-UA 105) and Mathematical Physics (PHYS-UA 106). Offered every year. 3 points.

Topics include relation of entropy to probability and energy to temperature; the laws of thermodynamics; Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac statistics; equations of state for simple gases and chemical and magnetic systems; and elementary theory of phase transitions.

Astrophysics

PHYS-UA 150 Prerequisite: Physics III (PHYS-UA 95) or permission of the instructor. Offered every other year. 4 points.

Introduction to modern astrophysical problems with an emphasis on the physical concepts involved: radio, optical, and X-ray astronomy; stellar structure and evolution; white dwarfs, pulsars, and black holes; and galaxies, quasars, and cosmology.

Physics of Biology

PHYS-UA 160 Prerequisite: Physics III (PHYS-UA 95). Offered every other year. 3 points.

Using basic physical concepts such as energy, entropy, and force, explores biology from a different perspective. Presents a survey of basic biological processes at all levels of organization (molecular, cellular, organismal, and population) in the light of simple ideas from physics. To illustrate this approach, examines a few contemporary research topics, including self-assembly, molecular motors, low Reynolds fluid dynamics, optical imaging, and single-molecule manipulation. Attempts to construct links between fundamental concepts of biology and physics and to expose enormous open questions in the life sciences from the point of view of a physicist. Geared toward students with a background in mathematics and the physical sciences.

General Relativity

PHYS-UA 170 Prerequisite: Dynamics (PHYS-UA 120) or permission of the instructor. Offered in the spring. 3 points.

Provides an introduction to general relativity, stressing physical phenomena and their connection to experiments and observations. Topics include special relativity, gravity as geometry, black holes, gravitational waves, cosmology, Einstein equations.

PHYS-UA 180

Fluid dynamics is the branch of physics that describes motions of fluids as varied as the flow of blood in the human body, the flight of an insect or the motions of weather systems on Earth. The course introduces the key concepts of fluid dynamics: the formalism of continuum mechanics, the conservation of mass, energy and momentum in a fluid, the Euler and Navier-Stokes equations, viscosity and vorticity. These concepts are applied to study classic problems in fluid dynamics, such as potential flow around a cylinder, the Stokes flow, the propagation of sound and gravity waves and the onset of instability in shear flow.

Computational Physics

PHYS-UA 210 Prerequisites: Mathematical Physics (PHYS-UA 106) or permission of the instructor, and knowledge of a scientific programming language (such as C, C++, Fortran, or Python). Offered every year. 4 points.

Introduction to computational physics, with an emphasis on fields of current research interest in which numerical techniques provide unique physical insight. Topics are chosen from various branches of physics, including numerical solution of ordinary and partial differential equations, eigenvalue problems, Monte Carlo methods in statistical mechanics, field theory, dynamical systems, and chaos.

Special Topics in Physics

PHYS-UA 800 Prerequisites vary with the topic. Offered occasionally. 3 points.

Covers advanced topics or recent developments in physics. Detailed course descriptions are made available when topics are announced.

Independent Study

PHYS-UA 997, 998 Prerequisite: permission of the director of undergraduate studies. Offered in the fall and spring respectively. 2 to 4 points per term.

The Universe: Its Nature and History

PHYS-UA 7 Offered every year. 4 points.

Qualitative introduction to our understanding of the nature and evolution of the universe. Topics include the creation of the cosmos; its explosive evolution, present structure, and ultimate fate; the nature of stars and galaxies; the structure and evolution of our Milky Way; the birth, life, and eventual death of the solar system; our place and role in the universe; and the relationship of modern astronomical ideas to other cultural disciplines.

Origins of Astronomy

PHYS-UA 8 Identical to MEDI-UA 8. Offered every other year. 4 points.

Introduction to the historical development of astronomy, from earliest times through the Copernican revolution. Traces the changes in our perception of the heavens and the influences that led to those changes, from astrology to the discoveries of Galileo and the physics of Newton. Includes descriptive astronomy of the solar system and a trip to the Hayden Planetarium.

Sound and Music

PHYS-UA 10 Assumes high school-level mathematics background. Offered every year. 4 points.

Explores the production of musical sound and how it is perceived by us, dealing mainly with the physical basis of sound. Covers sound waves, resonance, how musical instruments produce sound, the concepts of scales and harmony, physical acoustics, physiological factors of perception, acoustics of auditoria, and sound recording and reproduction. Develops the necessary physics for the course, as needed.

General Physics I

PHYS-UA 11 Prerequisite: Calculus I (MATH-UA 121) or equivalent, or completion of the Mathematics for Economics I and II sequence (MATH-UA 211 and 212), or permission of the instructor. Lecture, laboratory, and recitation. Not open to students who have completed Physics I (PHYS-UA 91) with a grade of C- or better. Offered in the fall. 5 points.

Begins a two-semester introduction to physics intended primarily for preprofessional students and for those majoring in a science other than physics, although well-prepared students may wish to take the Physics I, II, III sequence for majors (with corequisite laboratories), below. Topics include kinematics and dynamics of particles; momentum, work, and energy; gravitation; circular, angular, and harmonic motion; mechanical and thermal properties of solids, liquids, and gases.

General Physics II

PHYS-UA 12 Prerequisite: General Physics I (PHYS-UA 11) with a grade of C- or better or permission of the department. Lecture, laboratory, and recitation. Offered in the spring. 5 points.

Continuation of General Physics I (PHYS-UA 11). Topics include electric charge, field, and potential; magnetic forces and fields; resistive, capacitive, and inductive circuits; electromagnetic induction; wave motion; electromagnetic waves; geometrical optics; interference, diffraction, and polarization of light; relativity; atomic and nuclear structure; elementary particle physics.

Observational Astronomy

PHYS-UA 13 Prerequisite: The Universe: Its Nature and History (PHYS-UA 7) or higher, or permission of the instructor for nonscience majors and minors; no prerequisite for science majors and minors or those who have satisfied the MAP Natural Science I requirement. Lecture and laboratory. Offered every year. 4 points.

Introduction to the theory and practice of technical amateur astronomy. The approach is hands-on, with weekly evening laboratory/observing sessions. Topics include astronomical coordinate systems, optics, how to use a telescope, and the phenomena that can be seen in the urban night sky. Observing sessions involve the use of eight-inch telescopes.

20th-Century Concepts of Space, Time, and Matter

PHYS-UA 20 Assumes high school-level geometry and intermediate algebra background. Not open to students who have completed Natural Science I: Einstein’s Universe (MAP-UA 204). Offered every year. 4 points.

The 20th century has been witness to two major revolutions in man’s concepts of space, time, and matter. Einstein’s special and general theories of relativity: implications of the special theory, for our understanding of the unity of space and time, and the general theory, for our understanding of the nature of gravity. Quantum mechanics: a new picture of the basic structure and interactions of atoms, molecules, and nuclei. Topics include the uncertainty principle, wave-particle duality, and the continuing search for the fundamental constituents of matter.

Introductory Experimental Physics I

PHYS-UA 71 Typically taken with Physics I (PHYS-UA 91). Offered in the fall. 2 points.

The first of two introductory-level laboratory courses. Introduces essential experimental techniques, including setup and operation of basic laboratory equipment, elementary experimental design, statistics and inference, and computational data analysis. Experimental techniques are introduced in the context of classic physics experiments.

Introductory Experimental Physics II

PHYS-UA 72 Prerequisite: Introductory Experimental Physics I (PHYS-UA 71). Typically taken with Physics II (PHYS-UA 93). Offered in the spring. 2 points.

Continuation of Introductory Experimental Physics I (PHYS-UA 71).

Intermediate Experimental Physics I

PHYS-UA 73 Prerequisite: Introductory Experimental Physics II (PHYS-UA 72). Typically taken with Physics III (PHYS-UA 95). Offered in the fall. 2 points.

The first of two intermediate-level laboratory courses. Develops further the experimental techniques introduced in Introductory Experimental Physics I, II (PHYS-UA 71, 72) in the context of more advanced experiments.

Intermediate Experimental Physics II

PHYS-UA 74 Prerequisite: Intermediate Experimental Physics I (PHYS-UA 73). Typically taken with Classical and Quantum Waves (PHYS-UA 105). Offered in the spring. 2 points.

Continuation of Intermediate Experimental Physics I (PHYS-UA 73).

Physics I

PHYS-UA 91 Corequisite: Calculus I (MATH-UA 121) or Honors Calculus I: Accelerated Calculus with Linear Algebra I (MATH-UA 221). Physics majors must also register for Introductory Experimental Physics I (PHYS-UA 71). Lecture and recitation. Offered in the fall. 3 points.

With PHYS-UA 93 and PHYS-UA 95, forms a three-semester sequence that must be taken in order, starting in the fall semester. Intended for physics majors and other interested science and mathematics majors. Topics include kinematics and dynamics of particles; energy and momentum; rotational kinematics and dynamics; harmonic oscillators; gravitational fields and potentials; special relativity.

Physics II

PHYS-UA 93 Prerequisite: Physics I (PHYS-UA 91) with a grade of C or better, or permission of the department. Corequisite: Calculus II (MATH-UA 122) or Honors Calculus II: Accelerated Calculus with Linear Algebra II (MATH-UA 222). Physics majors must also register for Introductory Experimental Physics II (PHYS-UA 72). Lecture and recitation. Offered in the spring. 3 points.

Continuation of Physics I (PHYS-UA 91). Topics include electrostatics; dielectrics; currents and circuits; the magnetic field and magnetic materials; induction; AC circuits; Maxwell’s equations.

Physics III

PHYS-UA 95 Prerequisite: Physics II (PHYS-UA 93) with a grade of C or better, or permission of the department. Corequisite: Calculus III (MATH-UA 123) or Honors Calculus II: Accelerated Calculus with Linear Algebra II (MATH-UA 222). Physics majors must also register for Intermediate Experimental Physics I (PHYS-UA 73). Lecture and recitation. Offered in the fall. 3 points.

Continuation of Physics II (PHYS-UA 93). Topics include wave motion; Fourier series; sound; the reflection, refraction, interference, and diffraction of light; polarization; thermodynamics; kinetic theory and statistical physics.

Classical and Quantum Waves

PHYS-UA 105 Prerequisite: Physics III (PHYS-UA 95), and either Calculus III (MATH-UA 123) or Honors Calculus II: Accelerated Calculus with Linear Algebra II (MATH-UA 222). Physics majors must also register for Intermediate Experimental Physics II (PHYS-UA 74). Lecture and recitation. Offered in the spring. 3 points.

Topics include linear and nonlinear oscillators, resonance, coupled oscillators, normal modes, mechanical waves, light, matter waves, Fourier analysis, Fourier optics (diffraction), and an introduction to numerical (computer) methods for solving differential equations.

Mathematical Physics

PHYS-UA 106 Prerequisite: Physics III (PHYS-UA 95). Lecture and recitation. Offered in the spring. 3 points.

Mathematical preparation for the junior and senior courses in physics. Vector analysis, Fourier series and integrals, ordinary differential equations, matrices, partial differential equations, and boundary-value problems.

Electronics for Scientists

PHYS-UA 110 Identical to BIOL-UA 110, CHEM-UA 671. Prerequisite: General Physics II (PHYS-UA 12) or Physics II (PHYS-UA 93) or permission of the instructor. Lecture and laboratory. Offered in the fall. 5 points.

Introduction to basic analog and digital electronics used in modern experiments and computers, for students from any science discipline. Basic concepts and devices presented in lecture are studied in the laboratory. Topics include filters, power supplies, transistors, operational amplifiers, digital logic gates, and both combinatorial and sequential digital circuits. Students learn the functions of modern electronic instrumentation and measurement.

Advanced Experimental Physics

PHYS-UA 112 Prerequisites: Intermediate Experimental Physics I, II (PHYS-UA 73, 74) and Quantum Mechanics I (PHYS-UA 123), or permission of the instructor. Laboratory. Offered every year. 3 points.

Introduces the experiments and techniques of modern physics. Students choose their experiments and may use microcomputers for data analysis. Experimental areas include optical spectroscopy, the Mössbauer effect, cosmic rays, magnetic resonance, condensed matter, and relativistic mass.

Dynamics

PHYS-UA 120 Prerequisites: Physics III (PHYS-UA 95) and Mathematical Physics (PHYS-UA 106). Offered every year. 3 points.

Intermediate-level course on the principles and applications of dynamics. Emphasis on the formulation of problems and their numerical solution. Topics include conservation laws, central force motion, Lagrange’s and Hamilton’s equations, normal modes and small oscillations, and accelerated reference frames.

Quantum Mechanics I

PHYS-UA 123 Prerequisite: Classical and Quantum Waves (PHYS-UA 105). Offered every year. 3 points.

Introduction to the experimental basis and formal mathematical structure of quantum mechanics. Topics include foundational experiments, wave-particle duality, wave functions, the uncertainty principle, the time-independent Schrödinger equation and its applications to one-dimensional problems and the hydrogen atom, angular momentum, and spin; Hilbert Space, operators, and observables; time-independent perturbation theory; atomic spectra.

Quantum Mechanics II

PHYS-UA 124 Prerequisite: Quantum Mechanics I (PHYS-UA 123). Offered every year. 3 points.

Continuation of Quantum Mechanics I (PHYS-UA 123). Topics include the time-dependent Schrödinger equation, the Schrödinger and Heisenberg description of quantum systems, time-dependent perturbation theory, scattering theory, quantum statistics, and applications to atomic, molecular, nuclear, and elementary particle physics.

Electricity and Magnetism I

PHYS-UA 131 Prerequisites: Classical and Quantum Waves (PHYS-UA 105) and Mathematical Physics (PHYS-UA 106). Offered every year. 3 points.

Introduction to electrodynamics with applications to physical problems. Topics include electrostatics, magnetostatics, Maxwell’s equations, electromagnetic forces, electromagnetic waves, radiation from accelerating charges and currents, and special relativity.

Electricity and Magnetism II

PHYS-UA 132 Prerequisite: Electricity and Magnetism I (PHYS-UA 131). Offered every year. 3 points.

Continuation of Electricity and Magnetism I (PHYS-UA 131), with greater depth and emphasis on more complex phenomena and applications. Topics include solutions to the Laplace and Poisson equations, dielectrics and magnetic materials, gauge invariance, plasmas, Fresnel equations, transmission lines, wave guides, and antennas.

Optics

PHYS-UA 133 Prerequisite: Classical and Quantum Waves (PHYS-UA 105) or permission of the instructor. 3 points.

Introduction to physical and geometrical optics. Wave phenomena including diffraction, interference, first-order and higher-order coherence. Holography, phase contrast and atomic force microscopy, and limits of resolution are some of the subjects included. Topics include atomic energy levels and radiative transitions, and detectors from photon counting to bolometers for infrared radiation.

Condensed Matter Physics

PHYS-UA 135 Prerequisite: Classical and Quantum Waves (PHYS-UA 105) or permission of the instructor. Offered every other year. 3 points.

Designed as an introduction to condensed matter physics for students with knowledge of elementary quantum mechanics. Topics include crystal structure, lattice vibrations, and the energy band theory of metals and semiconductors; the electronic, magnetic, and optical properties of solids; and some modern research topics, such as the physics of nano-structures, soft condensed matter physics, and superconductivity.

Readings in Particle Physics

PHYS-UA 136 Prerequisite: Classical and Quantum Waves (PHYS-UA 105). Offered every other year. 3 points.

Particle physics is the study of the very fundamental constituents of matter and of the forces between them. By its nature it is microscopic, but it also connects with astrophysics and cosmology on the largest scales. This course introduces the most important advances in elementary particle physics. It centers on journal articles in which these advances were first published, with overview lectures, original reading, discussion, and student presentations. Topics include the discovery of elementary particles in cosmic rays, antimatter, symmetries found in nature, and the invention of the Quark model of elementary particles and its experimental verification.

Thermal and Statistical Physics

PHYS-UA 140 Prerequisites: Classical and Quantum Waves (PHYS-UA 105) and Mathematical Physics (PHYS-UA 106). Offered every year. 3 points.

Topics include relation of entropy to probability and energy to temperature; the laws of thermodynamics; Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac statistics; equations of state for simple gases and chemical and magnetic systems; and elementary theory of phase transitions.

Astrophysics

PHYS-UA 150 Prerequisite: Physics III (PHYS-UA 95) or permission of the instructor. Offered every other year. 4 points.

Introduction to modern astrophysical problems with an emphasis on the physical concepts involved: radio, optical, and X-ray astronomy; stellar structure and evolution; white dwarfs, pulsars, and black holes; and galaxies, quasars, and cosmology.

Physics of Biology

PHYS-UA 160 Prerequisite: Physics III (PHYS-UA 95). Offered every other year. 3 points.

Using basic physical concepts such as energy, entropy, and force, explores biology from a different perspective. Presents a survey of basic biological processes at all levels of organization (molecular, cellular, organismal, and population) in the light of simple ideas from physics. To illustrate this approach, examines a few contemporary research topics, including self-assembly, molecular motors, low Reynolds fluid dynamics, optical imaging, and single-molecule manipulation. Attempts to construct links between fundamental concepts of biology and physics and to expose enormous open questions in the life sciences from the point of view of a physicist. Geared toward students with a background in mathematics and the physical sciences.

General Relativity

PHYS-UA 170 Prerequisite: Dynamics (PHYS-UA 120) or permission of the instructor. Offered in the spring. 3 points.

Provides an introduction to general relativity, stressing physical phenomena and their connection to experiments and observations. Topics include special relativity, gravity as geometry, black holes, gravitational waves, cosmology, Einstein equations.

**Introduction to Fluid Dynamics**PHYS-UA 180

*Identical to MATH-UA 230. Prerequisites: Calculus III (MATH-UA 123); Mathematical Physics (PHYS-UA 106) is suggested. Offered every year. 4 points.*Fluid dynamics is the branch of physics that describes motions of fluids as varied as the flow of blood in the human body, the flight of an insect or the motions of weather systems on Earth. The course introduces the key concepts of fluid dynamics: the formalism of continuum mechanics, the conservation of mass, energy and momentum in a fluid, the Euler and Navier-Stokes equations, viscosity and vorticity. These concepts are applied to study classic problems in fluid dynamics, such as potential flow around a cylinder, the Stokes flow, the propagation of sound and gravity waves and the onset of instability in shear flow.

Computational Physics

PHYS-UA 210 Prerequisites: Mathematical Physics (PHYS-UA 106) or permission of the instructor, and knowledge of a scientific programming language (such as C, C++, Fortran, or Python). Offered every year. 4 points.

Introduction to computational physics, with an emphasis on fields of current research interest in which numerical techniques provide unique physical insight. Topics are chosen from various branches of physics, including numerical solution of ordinary and partial differential equations, eigenvalue problems, Monte Carlo methods in statistical mechanics, field theory, dynamical systems, and chaos.

Special Topics in Physics

PHYS-UA 800 Prerequisites vary with the topic. Offered occasionally. 3 points.

Covers advanced topics or recent developments in physics. Detailed course descriptions are made available when topics are announced.

Independent Study

PHYS-UA 997, 998 Prerequisite: permission of the director of undergraduate studies. Offered in the fall and spring respectively. 2 to 4 points per term.