Download MIT Physics Graduate General Exams

MIT Physics Graduate General Exams
Part I Concepts
Students studying for the Fall 2003 Part I exam found it useful to first categorize each problem by
the concept they thought was being tested. Such an approach simplified their subsequent attempt
at solving the problem. The following is a list of all the concepts they thought could be used as
the basis for Part I problems. Faculty who have reviewed the list believe that it is essentially
complete.
Classical Mechanics
Conservation of momentum, energy, and angular momentum
Harmonic motion
Normal modes
Coupled systems
Coriolis effect
Central force motion
Rocket motion
Wave motion (group and phase velocities)
Resonance
Gyroscopes
Lagrange equations
Hamilton's equations
Fluid dynamics
Electricity and Magnetism
Maxwell's equations: Gauss’s, Ampere's and Faraday's Laws
Superpostion
Boundary conditions
Dielectrics
Radiation
Energy of fields
Laplace's equation and the wave equation
Time relationship of B(t) and E(t)
Circuits: RLC analog circuits
Poynting vectors
Retarded potentials
Interference
Diffraction
Waveguides and resonators
Quantum Mechanics
Manipulation of Schrodinger’s Equation
Expansions and superpositions
Addition of angular momentum
Non-degenerate time independent perturbation theory
Degenerate time independent perturbation theory
Stark Shift, Zeeman effect, and spin-orbit coupling
Quantum statistics: Boson/Fermion properties
Adiabatic and sudden approximations
Reflection and transmission
Bohr Model
Hydrogen atomic structure
Atomic notation
Very basic scattering problems
General solutions to HO and well problems
Probability conservation
Statistical Mechanics and Thermodynamics
Maxwell's relations
Laws of thermodynamics
Microcanonical ensemble
Canonical ensemble
Grand canonical ensemble - chemical potential as a function of temperature
Partition functions
Statistics
Global entropy problems
Partial derivative math
State functions
Blackbody radiation
Bose/Fermi/Maxwell statistics
Carnot cycles
Ideal gas
Specific heat
Degrees of freedom
Special Relativity
Four vectors
Lorentz transformations
Doppler shift
Velocity addition
Relativistic energy and momentum
Optics
Geometrical optics
Index of refraction (n) and its physical origin
Interference and diffraction (Huygen's Prin.)