Quantum & Atomic Physics

A fundamental physical constant expressing the limiting wavenumber of atomic spectral lines for infinitely heavy nuclei.

R_∞ = (m_e e⁴) / (8 ε₀² h³ c) ≈ 1.097373 × 10⁷ m⁻¹ m⁻¹ (Reciprocal Meters)

A fundamental partial differential equation describing how the quantum wave function of a physical system evolves deterministically over…

i ℏ (∂ψ / ∂t) = Ĥ ψ, Ĥ ψ = E ψ Energy (Eigenvalue E in Joules or eV)

Quantum & Atomic Physics

A set of quantum mechanical rules constraining allowed radiative transitions between atomic energy states.

Δl = ±1, Δm_l = 0, ±1 Dimensionless Quantum Rules

Quantum & Atomic Physics

A relativistic quantum interaction between an electron's intrinsic spin magnetic moment and the internal magnetic field created by its…

H_SO = ξ(r) L · S eV (Energy Shift)

Quantum & Atomic Physics

The process by which an excited atom or quantum system spontaneously decays to a lower energy state, emitting a photon of random phase and…

Rate = A₂₁ N₂ s⁻¹ (Transition Rate)

Quantum & Atomic Physics

The shifting and splitting of atomic spectral lines caused by the presence of an external static electric field.

ΔE = -p · E_ext (First-order: ΔE ∝ E_ext) eV (Energy Shift)

Quantum & Atomic Physics

A landmark 1922 experiment that proved space quantization and the intrinsic angular momentum (spin) of subatomic particles.

F_z = μ_z (∂B_z / ∂z), S_z = ± ℏ / 2 N (Force), J/T (Magnetic Moment)

Quantum & Atomic Physics

The process in which an incoming photon stimulates an excited atom to drop to a lower state, emitting a second identical photon.

Rate = B₂₁ ρ(ν) N₂ s⁻¹ (Transition Rate)

Quantum & Atomic Physics

A complex-valued mathematical function containing all the physical information about the state of an isolated quantum mechanical system.

ψ(x, t) = A e^(i (k x - ω t)) m^(-3/2) (in 3D space)

Quantum & Atomic Physics

The fundamental quantum mechanical principle stating that every subatomic entity exhibits both wave-like and particle-like behavior…

E = h ν, p = h / λ Dimensionless Concept

Quantum & Atomic Physics

The splitting of atomic spectral lines into multiple closely spaced components in the presence of an external static magnetic field.

ΔE = g_L μ_B m_j B eV (Energy Shift)

Quantum & Atomic Physics

The lowest possible quantum mechanical energy state that a physical system may possess at absolute zero temperature (0 K).

E₀ = ½ ℏ ω (for harmonic oscillator) eV or Joules