## The Path to The Ph.D

The Georgetown graduate experience is tailored to match your academic and professional goals. The process is straight-forward, but as with any program, there are certain benchmarks that help you chart your path. Detailed information is available in the Graduate Handbook.

- Perform well and earn 34 credits in the coursework (maintain a GPA of 3.0 or above)
- Participate in the Integrative Experience after the 1
^{st}2 semesters of coursework - Join 3 Lab Rotations to gain expertise and choose an Academic Advisor
- Pass the Comprehensive Examination, typically before beginning their 2
^{nd}year - Pass the Qualifying Examination, within 18 months of completing coursework or directly after an Apprenticeship
- Research, write and defend a Dissertation

## Prerequisites for first-year graduate courses

### Classical mechanics

- Lagrangian formulation at the level of Marion.
- Understand the definition of Hamiltonian and of a Poisson bracket.

### COMPUTATIONAL AND MATHEMATICAL PHYSICS

- Proficiency in coding in a high-level programming language like Fortran, C, C++, or java.
- Understanding loops and conditional statements.
- Full knowledge of how to solve second order differential equations with constant coefficients.
- Separation of variables for partial differential equations.
- Familiarity with the classic differential equations:
- Heat flow or diffusion,
- Wave or Schroedinger equation, and
- Boundary-value problems.

- Understanding of Fourier analysis (both discrete and a continuous Fourier transform) and eigenvalue problems.

### ELECTROMAGNETISM

- Differential formulation of Maxwell’s equations
- Poisson’s equation
- Multipole expansions
- Generation of electromagnetic waves
- Circuit analysis (both AC and DC)
- Geometrical & physical optics, (at the level of Griffiths).

### Quantum mechanics

- Bra and ket notation
- Eigenvalue problems (as partial differential equations and in matrix form)
- Separation of variables
- Raising and lowering operators
- Addition of angular momentum
- Spin
- Hydrogen atom
- Nondegenerate perturbation theory
- Simple time-evolution problems (at the level of Liboff, Griffiths, or Dicke and Witte).

### Statistical mechanics

- Definitions of entropy, free energy, chemical potential.
- Free energy of classical and quantum harmonic oscillator.
- Equipartition theorem.
- Degenerate Fermi and Bose gases.
- One-dimensional Ising model. (At the level of Kittel and Kroemer).