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# Physics GRE 5. Quantum Mechanics and Atomic Physics

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5.1 Average Value of Operator, "A", on state psi
5.2 Position-Probability Normalization of state psi
5.3 Property of Hermitian Operator "Q" acting on states f and g
5.4 Position and Momentum Operators
5.5 Probability of Obtaining nth eigenvalue
5.6 Expectation (Average) Value
5.7 Inner product of and a and b (Bracket Notation)
5.8 Bracket Notation Inner product commutative property
5.9 Hermitian Conjugate Condition for inner product
5.10 f(x), inner product relation for continuum states
5.11 inner product relation for states f,g with continuous position locations x
5.12 Schrodinger Equation
5.13 Hamiltonian Operator
5.14 Schrodinger, Eigenvalue Equation
5.15 Position, Momentum commutation relation
5.16 Uncertainty relation of operators A and B based off of their commutator
5.17 Statistical variance/ Uncertainty
5.18 Uncertainty Product for position and momentum
5.19 Order of Magnitude estimate of position and momentum uncertainty
5.20 Energy and Time order of magnitude momentum and position uncertainty
5.21 One Dimensional Harmonic Oscillator Hamiltonian
5.22 One dimensional Harmonic Oscillator Hamiltonian using raising and lowering operators
5.23 Commutation relation of lowering and raising operators
5.24 One Dimensional Harmonic Oscillator Energy Eigenvalues
5.25 Virial's Theorem for Harmonic Oscillator
5.26 Three Dimensional Harmonic Oscillator Energy Eigenvalues
5.27 Eigenfunctions and Energy Eigenvalues of a free particle
5.28 De Broglie Formula
5.29 Einstein's relation (energy of a free particle)
5.30 General Hamiltonian in Three Dimensions
5.31 3 Dimensional, position-momentum commutation along same direction
5.32 3 Dimensional, position-momentum commutation along different directions
5.33 Radial Wave function Normalization conditions
5.34 x component of orbital angular momentum
5.35 y component of orbital angular momentum
5.36 z component of orbital angular momentum
5.37 Commutator relation of orthogonal components of orbital angular momentum
5.38 Total orbital angular momentum
5.39 Z component of angular momentum acting on a spherical harmonic state
5.40 Total orbital angular momentum acting on a spherical harmonic state
5.41 Allowed values of m (magnetic moment) in terms of l (orbital angular momentum)
5.42 Orthonormaility of Spherical Harmonics
5.43 Hamiltonian of Hydrogen Atom
5.45 Un-normalized Ground state of Hydrogen Atom
5.46 Hydrogen Ground State Energy
5.47 nth Energy Eigenvalues of Hydrogen considering quantum number n only
5.48 fine structure constant
5.49 spin up and down along x in the z basis
5.50 spin up and down along y in z basis
5.51 Raising and Lowering Operators for spin 1/2 in terms of spin along x and y
5.54 Adding spins s and s'
5.55 Adding z component of spin quantum number m
5.56 Singlet State a system of 2 spin 1/2 particles
5.57 Perturbation Theory, 1st order energy Shift
5.58 Perturbation Theory, 2nd order energy shift
5.59 Eigenvalues of Spin-Orbit Operator, fine structure perturbation
5.60 Change in Hamiltonian from Stark Effect
5.61 Change in Hamiltonian for Zeeman Effect