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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.)