Physics Master's Program (with Thesis) (M.S., 1 - 2 Years)

The student agrees on a dissertation topic with an adviser from among the faculty members of the Physics Department, by the end of the first semester. The dissertation should include an introduction part covering the theory and literature on the topic, research part, results, discussion part, and a conclusion of the dissertation. The dissertation must be defended under oral examination conditions.

Presentation of more advanced mathematical language of modern physics foundations: linear algebra, ordinary differential equation and complex calculus. Special functions, complete orthonormal sets of functions. Hilbert Space. Calculus on curved and tangent spaces, Vector fields, Flows. Differential forms and exterior derivatives, Stock's theorem, Modern formulation of Maxwell theory. Distributions and Green's functions. Stability problems and numerical solutions at some non-linear problems. Each topic is exemplified with applications.

Introduction and review of Newton’s Laws of Mechanics. Motion of particles on the rotating Earth, Centrifugal and Coriolis forces. Calculus of Variations and its application to Mechanics. Generalized coordinates, Lagrangian and Hamiltonian Formalisms. The Two-Body Central Force Problem. Particle Trajectories (Orbits) of test particles in a gravitating central source. Simple analysis of the stability of motion. Moment of Inertia Matrix and its use in Rigid Body Motion. Symmetrical Top as an example of rigid body. Euler Angles and Rotation Matrices. Canonical Transformations, their physical meaning and Poisson Brackets.

Introduction to electrostatics. Coulomb’s Law as a Maxwell equation. Curl, Divergence, Laplace equation in Cartesian, Spherical and Cylindrical coordinates. Dirac delta function as a distribution in physics. Green’s and Gauss’s Divergence Theorems. Charge distributions and their associated potentials and Electric fields. Boundary value problems of electrostatics with applications to planar, rectangular, spherical and cylindrical problems. Legendre, Bessel functions and the idea of Green’s functions in electrostatics. Boundary value problems with dielectrics. Static Magnetic problem of a current.

Basic postulates of quantum mechanics, modification of classical concepts. Schrodinger equation and its solutions for simple systems, potential barrier, harmonic oscillator. Mathematical structure of quantum mechanics, wavefunctions, observables, operators, uncertainty principle, Schrodinger vs. Heisenberg representation. Angular momentum, motion in spherically symmetric potentials, hydrogen atom, spin, statistics and Pauli exclusion principle. Approximation methods, variational method, semiclassical approximation, perturbation theories.

This is an advanced seminar course that will be given by Master Students in Physics based on their research interest. A MS student must register this course until the end of the third semester.