Key Equations in Quantum Mechanics and Spectroscopy

Planck's Equation (Photon Energy)

E=hν

Wave Frequency-Wavelength Relation

ν=λ/c

Wavenumber Definition

ν~ = 1/λ

de Broglie Wavelength

λ= h/(mv)

Photoelectric Equation

E_k = hν − ϕ

Time-Independent Schrödinger Equation

H^ψ = Eψ

Heisenberg Uncertainty Principle

ΔxΔp ≥ ℏ/2

Particle in a Box Energy Levels

E_n PIB = (n^2 h^2)/(8mL^2)

Rigid Rotor Energy (Rotational Energy Levels)

E_{ml} RR = (ℏ^2 m_l^2)/(2I)

Harmonic Oscillator Energy

E_v HO = (v + 1/2)hν

Vibrational Frequency of a Harmonic Oscillator

ν = (1/(2π))√(k_f/m)

Hydrogen Atom Energy Levels

E_n H = - (hcR_H)/(n^2)

Addition of Orbital Angular Momentum

L = l_1 + l_2, l_1 + l_2 - 1, ..., |l_1 - l_2|

Addition of Spin Angular Momentum

S = s_1 + s_2, s_1 + s_2 - 1, ..., |s_1 - s_2|

Total Angular Momentum Quantum Number

J = L + S, L + S - 1, ..., |L - S|

Spectroscopic Term Symbol Calculation Parameter

b = (1/2)(N - N^*)