Physics GRE 5. Quantum Mechanics and Atomic Physics Essay

question

5.1 Average Value of Operator, “A”, on state psi
answer

question

5.2 Position-Probability Normalization of state psi
answer

question

5.3 Property of Hermitian Operator “Q” acting on states f and g
answer

question

5.4 Position and Momentum Operators
answer

question

5.5 Probability of Obtaining nth eigenvalue
answer

question

5.6 Expectation (Average) Value
answer

question

5.7 Inner product of and a and b (Bracket Notation)
answer

question

5.8 Bracket Notation Inner product commutative property
answer

question

5.9 Hermitian Conjugate Condition for inner product
5.9 Hermitian Conjugate Condition for inner product
answer

question

5.10 f(x), inner product relation for continuum states
answer

question

5.11 inner product relation for states f,g with continuous position locations x
5.11 inner product relation for states f,g with continuous position locations x
answer

question

5.12 Schrodinger Equation
answer

question

5.13 Hamiltonian Operator
5.13 Hamiltonian Operator
answer

question

5.14 Schrodinger, Eigenvalue Equation
answer

question

5.15 Position, Momentum commutation relation
answer

question

5.16 Uncertainty relation of operators A and B based off of their commutator
answer

question

5.17 Statistical variance/ Uncertainty
answer

question

5.18 Uncertainty Product for position and momentum
answer

question

5.19 Order of Magnitude estimate of position and momentum uncertainty
5.19 Order of Magnitude estimate of position and momentum uncertainty
answer

question

5.20 Energy and Time order of magnitude momentum and position uncertainty
answer

question

5.21 One Dimensional Harmonic Oscillator Hamiltonian
answer

question

5.22 One dimensional Harmonic Oscillator Hamiltonian using raising and lowering operators
answer

question

5.23 Commutation relation of lowering and raising operators
answer

question

5.24 One Dimensional Harmonic Oscillator Energy Eigenvalues
answer

question

5.25 Virial’s Theorem for Harmonic Oscillator
answer

question

5.26 Three Dimensional Harmonic Oscillator Energy Eigenvalues
5.26 Three Dimensional Harmonic Oscillator Energy Eigenvalues
answer

question

5.27 Eigenfunctions and Energy Eigenvalues of a free particle
answer

question

5.28 De Broglie Formula
5.28 De Broglie Formula
answer

question

5.29 Einstein’s relation (energy of a free particle)
answer

question

5.30 General Hamiltonian in Three Dimensions
answer

question

5.31 3 Dimensional, position-momentum commutation along same direction
5.31 3 Dimensional, position-momentum commutation along same direction
answer

question

5.32 3 Dimensional, position-momentum commutation along different directions
answer

question

5.33 Radial Wave function Normalization conditions
answer

question

5.34 x component of orbital angular momentum
answer

question

5.35 y component of orbital angular momentum
5.35 y component of orbital angular momentum
answer

question

5.36 z component of orbital angular momentum
answer

question

5.37 Commutator relation of orthogonal components of orbital angular momentum
answer

question

5.38 Total orbital angular momentum
answer

question

5.39 Z component of angular momentum acting on a spherical harmonic state
answer

question

5.40 Total orbital angular momentum acting on a spherical harmonic state
answer

question

5.41 Allowed values of m (magnetic moment) in terms of l (orbital angular momentum)
5.41 Allowed values of m (magnetic moment) in terms of l (orbital angular momentum)
answer

question

5.42 Orthonormaility of Spherical Harmonics
5.42 Orthonormaility of Spherical Harmonics
answer

question

5.43 Hamiltonian of Hydrogen Atom
answer

question

5.44 Bohr Radius
answer

question

5.45 Un-normalized Ground state of Hydrogen Atom
answer

question

5.46 Hydrogen Ground State Energy
answer

question

5.47 nth Energy Eigenvalues of Hydrogen considering quantum number n only
answer

question

5.48 fine structure constant
5.48 fine structure constant
answer

question

5.49 spin up and down along x in the z basis
answer

question

5.50 spin up and down along y in z basis
answer

question

5.51 Raising and Lowering Operators for spin 1/2 in terms of spin along x and y
answer

question

5.54 Adding spins s and s’
answer

question

5.55 Adding z component of spin quantum number m
5.55 Adding z component of spin quantum number m
answer

question

5.56 Singlet State a system of 2 spin 1/2 particles
answer

question

5.57 Perturbation Theory, 1st order energy Shift
answer

question

5.58 Perturbation Theory, 2nd order energy shift
5.58 Perturbation Theory, 2nd order energy shift
answer

question

5.59 Eigenvalues of Spin-Orbit Operator, fine structure perturbation
answer

question

5.60 Change in Hamiltonian from Stark Effect
answer

question

5.61 Change in Hamiltonian for Zeeman Effect
answer

Get instant access to
all materials

Become a Member