Noah Graham
William R. Kenan, Jr. Professor of Physics

- Office
- McCardell Bicen Hall 533
- Tel
- (802) 443-3423
- ngraham@middlebury.edu
- Office Hours
- Spring 2023: Monday 10:00--11:00 AM, Wednesday, 2:30--3:30 PM, and Friday, 1:30--2:30 PM, and by appointment
- Additional Programs
- Academic Affairs Physics
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Courses Taught
CSCI 0450
Fourier Signal Processing
Course Description
Fourier Analysis and Signal Processing
A wide range of computational applications involve oscillating signals in one or more dimensions. Fourier analysis techniques make it possible to analyze these signals in terms of the frequency components that make them up, forming the basis for technologies ranging from audio and video compression to sound and image processing to automatic speech and image recognition. In this course we will introduce the mathematics of Fourier series and transforms, their discretization through the Fast Fourier Transform, and associated topics such as convolutions, filters, and uncertainty relations. We will then apply these techniques to a variety of examples, including music, speech, and images. (MATH 0122 and MATH 0200 and CSCI 0201) 3 hrs. lect./lab
Terms Taught
Requirements
FYSE 1214
Space, Time, & Measurement
Course Description
Space, Time, and Measurement
The ability to precisely measure distance and time is essential to modern science and technology. Improvements in the technology of measurement made possible scientific discoveries that then redefined our fundamental understanding of space, time and measurement themselves. We’ll follow this process, from Galileo’s pendulum through Einstein’s theory of relativity to modern applications in quantum mechanics and cosmology, using historical and scientific texts, analytic writing, and a few hands-on activities to understand these ideas and their impact on science and society. 3 hr. sem.
Terms Taught
Requirements
INTD 0500
Independent Study
Course Description
Independent Study
Approval Required
Terms Taught
PHYS 0110
Current
Electricity & Magnetism
Course Description
Electricity and Magnetism
The physical principles of electricity and magnetism are developed with calculus and applied to the electrical structure of matter and the electromagnetic nature of light. Practical topics from electricity and magnetism include voltage, current, resistance, capacitance, inductance, and AC and DC circuits. Laboratory work includes an introduction to electronics and to important instruments such as the oscilloscope. (PHYS 0109, MATH 0122) 3 hrs. lect./3 hrs. lab.
Terms Taught
Requirements
PHYS 0212
Current
Applied Math For Phys. Science
Course Description
Applied Mathematics for the Physical Sciences
This course concentrates on the methods of applied mathematics used for treating the partial differential equations that commonly arise in physics, chemistry, and engineering. Topics include differential vector calculus, Fourier series, and other orthogonal function sets. Emphasis will be given to physical applications of the mathematics. This course is a prerequisite for all 0300- and 0400-level physics courses. (MATH 0122; PHYS 0110 concurrent or prior) 4.5 hrs. lect.
Terms Taught
Requirements
PHYS 0301
Intermediate Electromagnetism
Course Description
Intermediate Electromagnetism
The unified description of electricity and magnetism is one of the greatest triumphs of physics. This course provides a thorough grounding in the nature of electric and magnetic fields and their interaction with matter. Mathematical techniques appropriate to the solution of problems in electromagnetism are also introduced. The primary emphasis is on static fields, with the full time-dependent Maxwell equations and electromagnetic waves introduced in the final part of the course. (PHYS 0110; PHYS 0201 or by permission; PHYS 0212) 3 hrs. lect./1 hr. disc.
Terms Taught
PHYS 0350
Statistical Mechanics
Course Description
Statistical Mechanics
This course is a study of statistical mechanics and its applications to a variety of classical and quantum systems. It includes a discussion of microstates, macrostates, and entropy, and systematically introduces the microcanonical, canonical, grand canonical, and isobaric ensembles. This underlying theory is applied to topics including classical thermodynamics, the equipartition theorem, electromagnetic blackbody radiation, heat capacities of solids, and ideal classical and quantum gases, with a focus on Bose-Einstein condensation and degenerate Fermi systems. (PHYS 0202 and PHYS 0212) 3 hrs. lect.
Terms Taught
PHYS 0380
General Relativity
Course Description
General Relativity
Among the forces of nature, gravity is both the most familiar and the least well-understood. A hundred years after it was formulated by Einstein, General Relativity remains our best fundamental theory of gravity. In this course we will see how gravity emerges from the geometry of curved spacetime and how this picture leads to phenomena such as black holes, gravitational waves, and the expansion of the universe. (MATH 0200, PHYS 0201, and PHYS 0212) 3 hrs. lect.
Terms Taught
Requirements
PHYS 0401
Quantum Mechanics
Course Description
Quantum Mechanics
A fundamental course in quantum mechanics aimed at understanding the mathematical structure of the theory and its application to physical phenomena at the atomic and nuclear levels. Topics include the basic postulates of quantum mechanics, operator formalism, Schrödinger equation, one-dimensional and central potentials, angular momentum and spin, perturbation theory, and systems of identical particles. (PHYS 0202 and PHYS 0212; MATH 0200 recommended) 3 hrs. lect.
Terms Taught
PHYS 0500
Current
Upcoming
Ind. Study & Special Topic
Course Description
Independent Study and Special Topics
(Approval required)
Terms Taught
PHYS 0704
Upcoming
Senior Project
Course Description
Senior Project
Independent research project incorporating both written and oral presentations.
Terms Taught
PHYS 0705
Current
Upcoming
Senior Research & Thesis
Course Description
Senior Research and Thesis
Independent research in the fall, winter, and spring terms culminating in a written thesis (two units total). (Approval required)
Terms Taught
PHYS 1108
Quantum Mech./Linear Algebra
Course Description
Quantum Mechanics from Linear Algebra
The mysterious and surprising predictions of quantum mechanics, such as uncertainty in measurement and the failure of determinism, can be best understood through the language of linear algebra. In this course we will use eigenvectors and eigenvalues, dot products, and the Cauchy-Schwarz inequality to develop the fundamental postulates of quantum mechanics and their predictions for the behavior of quantum systems. We will focus particularly on spin systems, which have applications to areas ranging from quantum computing to magnetic resonance imaging to quaternion methods for 3-D graphics and motion tracking. No prior physics experience is assumed apart from basic familiarity with concepts such as momentum, energy, and electric charge. (MATH 0122, MATH 0200, and introductory physics at the high school or college level.)
Terms Taught
Requirements
Academic Degrees
A. B., Harvard University
Ph. D., Massachusetts Institute of Technology