## Amherst College Physics and Astronomy for 2015-16

### Physics

#### 109 Energy

We will develop the concept of energy from a Physics perspective. We will introduce the various forms that energy can take and discuss the mechanisms by which it can be generated, transmitted, and transformed. The law of conservation of energy will be introduced both as a useful tool, and as an example of a fundamental physical law. The environmental and financial costs and benefits of various methods of energy generation and consumption will be discussed. Demonstrations and hands-on laboratory experiences will be an integral part of the course. The course is intended for non-science majors and not for students who have either completed or intend to complete the equivalent of PHYS 117 or CHEM 110.

Requisite: A working knowledge of high-school algebra, geometry and trigonometry. Limited to 20 students. Spring semester. Professor Hunter.

**2015-16:**Offered in Spring 2016

**Other years:**Offered in Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2013, Spring 2014, Spring 2015

#### 114 Relativity, Cosmology, and Quantum Physics

This course will discuss Einstein's Special Theory of Relativity in quantitative detail, beginning with the roots of the principle of relativity in the writings of Galileo and Newton. We will then examine a qualitative outline of general relativity. We will next study the structure of matter and forces on the small scale and the challenges posed by the quantum theory, which provides the best description of the microworld. The last topic of the semester will be the application of relativity and quantum physics to the early universe. The course is designed for the non-specialist audience and will take an elementary but rigorous approach. No advanced mathematics or prior physics will be required; high school algebra and geometry will, however, be used extensively in class and in the problem sets. The work will require readings and regular problem sets, and students will also write a few essays.

Omitted 2015-16. Professor Jagannathan.

**2015-16:**Not offered

**Other years:**Offered in Fall 2008, Spring 2010, Fall 2011, Fall 2014

#### 116 Introductory Physics I: Mechanics and Wave Motion

The course will begin with a description of the motion of particles and introduce Newton’s dynamical laws and a number of important force laws. We will apply these laws to a wide range of problems to gain a better understanding of the laws and to demonstrate the generality of the framework. The important concepts of work, mechanical energy, and linear and angular momentum will be introduced and the unifying idea of conservation laws will be discussed. The study of mechanical waves permits a natural transition from the dynamics of particles to the dynamics of waves, including the interference of waves. Additional topics may include fluid mechanics and rotational dynamics. Three hours of lecture. Also one three-hour laboratory per week.

Requisite: MATH 111. Limited to 48 students. Fall semester: Professor Friedman. Spring semester: Professor TBA.

**2015-16:**Offered in Fall 2015 and Spring 2016

**Other years:**Offered in Fall 2007, Spring 2008, Fall 2008, Spring 2009, Fall 2009, Spring 2010, Fall 2010, Spring 2011, Fall 2011, Spring 2012, Fall 2012, Spring 2013, Fall 2013, Spring 2014, Fall 2014, Spring 2015

#### 117 Introductory Physics II: Electromagnetism and Optics

Most of the physical phenomena we encounter in everyday life are due to the electromagnetic force. This course will begin with Coulomb’s law for the force between two charges at rest and introduce the electric field in this context. We will then discuss moving charges and the magnetic interaction between electric currents. The mathematical formulation of the basic laws in terms of the electric and magnetic fields will allow us to work towards the unified formulation originally given by Maxwell. His achievement has, as a gratifying outcome, the description of light as an electromagnetic wave. The course will consider both ray-optics and wave-optics descriptions of light. Laboratory exercises will emphasize electrical circuits, electronic measuring instruments, optics and optical experiments. Three hours of lecture and discussion and one three-hour laboratory per week.

Requisite: PHYS 116 or 123. Limited to 48 students. Fall semester: Professor Carter. Spring semester: Professor TBA.

**2015-16:**Offered in Fall 2015 and Spring 2016

**Other years:**Offered in Fall 2007, Spring 2008, Fall 2008, Spring 2009, Fall 2009, Spring 2010, Fall 2010, Spring 2011, Fall 2011, Spring 2012, Fall 2012, Spring 2013, Fall 2013, Spring 2014, Fall 2014, Spring 2015

#### 119 Life at the Nanoscale

Our everyday intuitions about physics completely break down when thinking about life at the nanoscale. At this scale, biological molecules are large and Brownian motion and viscous friction dominate. Yet, to design the next generation of medical technologies, including nanobots that augment the immune system or destroy cancer cells, we need to understand the physics at this scale. In this course, we will learn about the physics behind random molecular motion and how to create nanoscale-directed movement using an engine. We will learn about how to build a microscope to visualize a nanomachine and the physical properties of polymers that might be useful as building materials. By the end of the course, students will have a working knowledge of physics at the molecular scale, important in nanotechnology and drug design. Three hours of lecture and three hours of laboratory per week; the laboratory projects will require additional time outside of class hours.

Requisite: PHYS 116. Limited to 20 students. Omitted 2015-16. Professor Carter.

**2015-16:**Not offered

#### 123 The Newtonian Synthesis: Dynamics of Particles and Systems, Waves

The idea that the same simple physical laws apply equally well in the terrestrial and celestial realms, called the Newtonian Synthesis, is a major intellectual development of the seventeenth century. It continues to be of vital importance in contemporary physics. In this course, we will explore the implications of this synthesis by combining Newton’s dynamical laws with his Law of Universal Gravitation. We will solve a wide range of problems of motion by introducing a small number of additional forces. The concepts of work, kinetic energy, and potential energy will then be introduced. Conservation laws of momentum, energy, and angular momentum will be discussed, both as results following from the dynamical laws under restricted conditions and as general principles that go well beyond the original context of their deduction. Newton’s laws will be applied to a simple continuous medium to obtain a wave equation as an approximation. Properties of mechanical waves will be discussed. Four hours of lecture and discussion and one three-hour laboratory per week.

Requisite: MATH 111. Limited to 24 students. Fall semester. Professor Hanneke.

**2015-16:**Offered in Fall 2015

**Other years:**Offered in Fall 2007, Fall 2008, Fall 2009, Fall 2010, Fall 2011, Fall 2012, Fall 2013, Fall 2014

#### 124 The Maxwellian Synthesis: Dynamics of Charges and Fields, Optics

In the mid-nineteenth century, completing nearly a century of work by others, Maxwell developed an elegant set of equations describing the dynamical behavior of electromagnetic fields. A remarkable consequence of Maxwell’s equations is that the wave theory of light is subsumed under electrodynamics. Moreover, we know from subsequent developments that the electromagnetic interaction largely determines the structure and properties of ordinary matter. The course will begin with Coulomb’s Law but will quickly introduce the concept of the electric field. Students will explore moving charges and their connection with the magnetic field, study currents and electrical circuits, and discuss Faraday’s introduction of the dynamics of the magnetic field and Maxwell’s generalization. Laboratory exercises will concentrate on circuits, electronic measuring instruments, and optics. Four hours of lecture and discussion and one three-hour laboratory per week.

Requisite: MATH 121 and PHYS 116 or 123. Limited to 24 students. Spring semester. Professor TBA.

**2015-16:**Offered in Spring 2016

**Other years:**Offered in Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015

#### 137 Quantum Mechanics of Two-Level Systems

Quantum Mechanics of Two-Level Systems: This course is designed for math and science students who are not majoring in physics but would like to learn the principles of quantum mechanics rigorously. For the most part, we will discuss the so-called two-level systems and collections of such systems. A two-level system has two basic states from which all other states may be constructed by linear combinations. We will begin with a review of linear algebra in two dimensions where the normalized vectors represent physical states and 2 x 2 matrices represent physical quantities and transformations. We will introduce the algebra of complex numbers as needed. Our prime examples will be an electron spin in an external field, and the various polarization states of the photon. Next we will consider a larger system that consists of several two-level subsystems. Though such a system is still very simple to describe, surprisingly, it exhibits nearly all the subtle and challenging features of the quantum theory. With the formalism developed, we will explore a range of foundational questions and applications such as uncertainty and measurement, entanglement, the EPR challenge and Bell’s theorem, the no-cloning theorem and teleportation. The work in the course comprises regular problem sets, two midterm exams and a final. Two meetings per week. Although the course will cover the necessary mathematics, some prior familiarity with vectors, matrices and basic linear algebra is useful.

Fall semester. Prof. Jagannathan.

Pending Faculty Approval.

**2015-16:**Offered in Fall 2015

#### 225 Modern Physics

The theories of relativity (special and general) and the quantum theory constituted the revolutionary transformation of physics in the early twentieth century. Certain crucial experiments precipitated crises in our classical understanding to which these theories offered responses; in other instances, the theories implied strange and/or counterintuitive phenomena that were then investigated by crucial experiments. After an examination of the basics of Special Relativity, the quantum theory, and the important early experiments, we will consider their implications for model systems such as a particle in a box, the harmonic oscillator, and a simple version of the hydrogen atom. We will also explore the properties of nuclei and elementary particles, study lasers and photonics, and discuss some very recent experiments of interest in contemporary physics. Three class hours per week.

Requisite: MATH 121 and PHYS 117 or 124. Fall semester. Professor Hall.

**2015-16:**Offered in Fall 2015

**Other years:**Offered in Fall 2007, Fall 2008, Fall 2009, Fall 2010, Fall 2011, Fall 2012, Fall 2013, Fall 2014

#### 226 Intermediate Laboratory

A variety of classic and topical experiments will be performed. In the area of fundamental constants, we will undertake a measurement of the speed of light, a determination of the ratio of Planck’s constant to the charge of the electron through the study of the photoelectric effect, and an experiment to obtain the charge-to-mass ratio of the electron. We will study the wave nature of the electron through a diffraction experiment. An experiment to measure optical spectra and another on gamma ray spectra will reveal the power of spectroscopy for exploring the structure of matter. Other experiments such as nuclear magnetic resonance, quantized conductance in nanocontacts, and properties of superconductors will give students an opportunity to experience laboratory practice in its contemporary form. Emphasis will be placed on careful experimental work and data-analysis techniques. One meeting a week of discussion plus additional, weekly self-scheduled laboratory work.

Requisite: PHYS 225 or consent of the instructor. Spring semester. Professor TBA.

**2015-16:**Offered in Spring 2016

**Other years:**Offered in Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015

#### 227 Methods of Theoretical Physics

The course will present the mathematical methods frequently used in theoretical physics. The physical context and interpretation will be emphasized. Topics covered will include vector calculus, complex numbers, ordinary differential equations (including series solutions), partial differential equations, functions of a complex variable, and linear algebra. Four class hours per week.

Requisite: MATH 121 and PHYS 117/124 or consent of the instructor. Fall semester. Professor Loinaz.

**2015-16:**Offered in Fall 2015

**Other years:**Offered in Fall 2007, Fall 2008, Fall 2009, Fall 2010, Fall 2011, Fall 2012, Fall 2013, Fall 2014

#### 230 Statistical Mechanics and Thermodynamics

The basic laws of physics governing the behavior of microscopic particles are in certain respects simple. They give rise both to complex behavior of macroscopic aggregates of these particles, and more remarkably, to a new kind of simplicity. Thermodynamics focuses on the simplicity at the macroscopic level directly, and formulates its laws in terms of a few observable parameters like temperature and pressure. Statistical Mechanics, on the other hand, seeks to build a bridge between mechanics and thermodynamics, providing in the process, a basis for the latter, and pointing out the limits to its range of applicability. Statistical Mechanics also allows one to investigate, in principle, physical systems outside the range of validity of Thermodynamics. After an introduction to thermodynamic laws, we will consider a microscopic view of entropy, formulate the kinetic theory, and study several pertinent probability distributions including the classical Boltzmann distribution. Relying on a quantum picture of microscopic laws, we will study photon and phonon gases, chemical potential, classical and degenerate quantum ideal gases, and chemical and phase equilibria. Three class hours per week.

Requisite: PHYS 225 or consent of the instructor. Spring semester. Professor TBA.

**2015-16:**Offered in Spring 2016

**Other years:**Offered in Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015

#### 343 Dynamics

This course begins with the foundation of classical mechanics as formulated in Newton’s Laws of Motion. We then use Hamilton’s Principle of Least Action to arrive at an alternative formulation of mechanics in which the equations of motion are derived from energies rather than forces. This Lagrangian formulation has many virtues, among them a deeper insight into the connection between symmetries and conservation laws. From the Lagrangian formulation we will move to the Hamiltonian formulation and the discussion of dynamics in phase space, exploring various avenues for the transition from the classical to the quantum theory. We will study motion in a central force field, the derivation of Kepler’s laws of planetary motion from Newton’s law of gravity, two-body collisions, and physics in non-inertial reference frames. Other topics may include the dynamics of driven, damped oscillators, and non-linear dynamics of chaotic systems. Three class hours per week.

Requisite: PHYS 227 or consent of the instructor. Fall semester. Professor Loinaz.

**2015-16:**Offered in Fall 2015

**Other years:**Offered in Fall 2007, Fall 2008, Fall 2009, Fall 2010, Fall 2011, Fall 2012, Fall 2013, Fall 2014

#### 347 Electromagnetic Theory I

A development of Maxwell’s electromagnetic field equations and some of their consequences using vector calculus. Topics covered include: electrostatics, steady currents and static magnetic fields, time-dependent electric and magnetic fields, and the complete Maxwell theory, energy in the electromagnetic field, Poynting’s theorem, electromagnetic waves, and radiation from time-dependent charge and current distributions. Three class hours per week.

Requisite: PHYS 117 or 124 and PHYS 227 or consent of the instructor. Fall semester. Professor Hall.

**2015-16:**Offered in Fall 2015

**Other years:**Offered in Fall 2007, Fall 2008, Fall 2009, Fall 2010, Fall 2011, Fall 2012, Fall 2013, Fall 2014

#### 348 Quantum Mechanics I

Wave-particle duality and the Heisenberg uncertainty principle. Basic postulates of Quantum Mechanics, wave functions, solutions of the Schroedinger equation for one-dimensional systems and for the hydrogen atom. Three class hours per week.

Requisite: PHYS 225 and 343 or consent of the instructor. Spring semester. Professor TBA.

**2015-16:**Offered in Spring 2016

**Other years:**Offered in Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015

#### 400 Molecular and Cellular Biophysics

(Offered as PHYS 400, BIOL 400, BCBP 400, and CHEM 400.) How do the physical laws that dominate our lives change at the small length and energy scales of individual molecules? What design principles break down at the sub-cellular level and what new chemistry and physics becomes important? We will answer these questions by looking at bio-molecules, cellular substructures, and control mechanisms that work effectively in the microscopic world. How can we understand both the static and dynamic shape of proteins using the laws of thermodynamics and kinetics? How has the basic understanding of the smallest molecular motor in the world, ATP synthase, changed our understanding of friction and torque? We will explore new technologies, such as atomic force and single molecule microscopy that have allowed research into these areas. This course will address topics in each of the three major divisions of Biophysics: bio-molecular structure, biophysical techniques, and biological mechanisms.

Requisite: CHEM 161, PHYS 116/123, PHYS 117/124, BIOL 191 or evidence of equivalent coverage in pre-collegiate courses. Spring semester. Professor TBA.

**2015-16:**Offered in Spring 2016

**Other years:**Offered in Spring 2008, Spring 2009, Spring 2011, Fall 2011, Fall 2012, Fall 2013, Spring 2015

#### 490 Special Topics

Independent Reading Course. A full course.

Fall and spring semester.

**2015-16:**Offered in Fall 2015 and Spring 2016

**Other years:**Offered in Fall 2007, Fall 2008, Fall 2009, Fall 2010, Fall 2011, Spring 2012, Fall 2012, Spring 2013, Fall 2013, Spring 2014, Fall 2014, Spring 2015

#### 498, 499, 499D Senior Departmental Honors

Individual, independent work on some problem, usually in experimental physics. Reading, consultation and seminars, and laboratory work. Designed for honors candidates, but open to other advanced students with the consent of the department.

Fall semester. The Department.

**2015-16:**Offered in Fall 2015

**Other years:**Offered in Fall 2007, Fall 2008, Fall 2009, Fall 2010, Fall 2011, Fall 2012, Fall 2013, Fall 2014