Quantum Mechanics Review Flashcards

Flashcards based on Quantum Mechanics lecture notes.

Bohr Postulate

L = m_evr = nħ, where n is an integer

De Broglie Wavelength

λ = h/p

Photon Energy

E = ħω = hc/λ

Energy of hydrogenic orbital

E = -RZ²/n²

Wavefunction Requirements

Single-valued, continuous (except possibly at infinite potential), normalizable (ψ → 0), differentiable/derivative continuous.

TISE

Ĥψ = Eψ

Expectation Value

⟨A⟩ = ∫ψ* A ψ dx

Heisenberg Uncertainty Principle

Δx Δp ≥ ħ/2

Particle in a 1D Box Energy

E = n²h² / 8mL², where n = 1, 2, …

Orthogonality

∫ψm* ψn dx = 0, for m ≠ n

Resonance Condition

hν = ΔE

Momentum Operator

p̂ = -iħ ∂/∂x

Commutator

[Â, B̂] = ÂB̂ - B̂Â

Harmonic Oscillator Energy

E(v) = (v + 1/2)ħω or (v+1/2)hν, where v = 0, 1, 2, …

and ω = √k/μ

Rigid Rotor Energy

E = ħ²J(J+1) / 2I, where J = 0, 1, 2, …

Quantization of Angular Momentum

J_z = m_Jħ, where m_J = -J, -J+1, …, J

Cyclic Boundary Condition

Ψ(φ + 2π) = Ψ(φ)

Spin Angular Momentum

|S| = ħ√(s(s+1)), S_z = m_sħ, where s = 1/2 and ms = ±1/2 for an electron.

Total Angular Momentum

j = l + s

Selection Rules

Δn = any, Δl = ±1, Δj = 0, ±1

Term Symbol

^(2S+1)L_J

Transmission Coefficient

T = 1 - R (for potential barrier scattering)

Spin-Orbit Coupling and j values

j can take values from |l-s| to l+s in integer steps… so l = 1 has j = ½ and j = 3/2… two energy values