Quantum Mechanics & Atomic Physics Flashcards
Expectation value of an observable

Probability of finding a particle somewhere

Hermitian operator facts

position and momentum operators

Expansion coefficient

Expectation value in a superposition of states

Definition of inner product behavior under complex conjugation of a bracket

Applying an operator to a bracket

Inner product on a function space

Time dependent Schrödinger equation

Hamiltonian operator



Commutator of the position and momentum operators

Generalized uncertainty principle

Variance

Uncertainty of position and momentum

“Folklore” uncertainty of x and p
ΔxΔp ≈ ħ
“Folklore” uncertainty of energy and time
ΔEΔt ≈ ħ
Hamiltonian for the quantum harmonic oscillator in one dimension

Hamiltonian for the quantum harmonic oscillator in one dimension in terms of raising and lowering operators

Commutation relation of the raising and lowering operators

Spectrum of the harmonic oscillator

Virial theorem

Energy of a harmonic oscillator in 3 dimensions

Wavefunction and energy of a free particle

de Broglie relation
p = ℏk = h/λ
Normalization of the radial part of the wavefunction

Normalization of the angular part of the wavefunction

Angular momentum operator in x

Angular momentum operator in y

Angular momentum operator in z









Hamiltonian of the hydrogen atom

Bohr radius

Scale of the ground state hydrogen wavefunction

Ground-state energy of a hydrogenic atom

Excited-state energy of hydrogenic atom

Fine structure constant

de Broglie wavelength
λ = h / p
Definition of a bra

Bohr theory energy to remove an electron from a single-electron, multi-proton atom
E=Z2E1
Products of operators [AB,C]
A[B,C] + [A,C]B
Products of operators [A,BC]
[A,B]C + B[A,C]
Raising/lowering normalization factors

Δt
The amount of time it takes the expectation value of Q to change by one standard deviation
If any observable changes rapidly, the uncertainty in energy must be large.




Spin raising and lower operators

Blackbody power spectrum

Stefan-Boltzmann law
dP / dA ∝ T4
Wavelength of the peak of a blackbody spectrum, given by Wien’s displacement law

Lz

Sz







Range of possible values for Lz

Number of allowed values for Lz
2l+1
Range of possible values for Sz

Range of possible values for Jz

Range of possible values for Lq

Range of possible values for Sq

Range of possible values for Jq

Selection rules for Δn
Δn = anything
Selection rules for Δl
Δl = ±1
Selection rules for Δml
Δml = 0, ±1
Selection rules for Δmj
Δmj = 0, ±1
ΔS’ selection rules for multi-electron atoms
ΔS’ = 0
Special selection rule for J of multi-electron atoms

Energies for particle in a box

Number of electrons in each full subshell
(2s+1)(2l+1)
2(2l+1) when s=1/2
Energy of a particle in an infinite box

Number of extrema in a harmonic oscillator wavefunction
n+1
Symmetry of a wavefunction with odd n
anti-symmetric
Symmetry of a wavefunction with even n
symmetric