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Quantum & Atomic Physics

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Quantum & Atomic Physics

Hydrogen Spectrum

The set of discrete electromagnetic emission and absorption lines produced when the electron in a hydrogen atom transitions between energy…

1 / λ = R_H (1 / n_f² - 1 / n_i²) m⁻¹ (Wavenumber) Quantum & Atomic Physics

Hyperfine Structure

Extremely small energy level splittings in atoms caused by interaction between nuclear magnetic moments and electron magnetic fields.

ΔE_HFS ∝ I_nucleus · J_electron eV or MHz (Small Energy Splitting) Quantum & Atomic Physics

Lamb Shift

A small energy difference between the 2s1/2 and 2p1/2 states of hydrogen caused by quantum vacuum fluctuations.

ΔE_Lamb ≈ 1057 MHz (for Hydrogen 2s1/2 and 2p1/2) MHz or eV Quantum & Atomic Physics

Laser Cooling

A technique using photon momentum from red-detuned laser beams to slow down moving gas atoms, cooling them to microkelvin temperatures.

F_force = ℏ k γ (I / I_sat) / (1 + 4 (Δ ± k v)² / γ²) μK or nK (Temperature) Quantum & Atomic Physics

Lyman Series

The hydrogen spectral series resulting from electron transitions dropping from higher excited states down to the ground state (n=1).

1 / λ = R_H (1 / 1² - 1 / n_i²), n_i = 2, 3, 4... Ultraviolet Wavelengths (nm) Quantum & Atomic Physics

Moseley's Law

An empirical law establishing a linear relationship between the square root of characteristic X-ray frequency emitted by an atom and its…

√ν = A (Z - b) Hz^(1/2) (Frequency Square Root) Quantum & Atomic Physics

Orbital Angular Momentum

The quantized angular momentum of a quantum particle associated with its orbital spatial motion around a central force field.

|L| = √(l (l + 1)) ℏ, L_z = m_l ℏ J·s (Angular Momentum Units) Quantum & Atomic Physics

Particle in a Box

A elementary quantum model describing a particle trapped inside a 1D rigid box with impenetrable potential barriers (infinite potential…

E_n = (n² π² ℏ²) / (2 m L²), ψ_n(x) = √(2/L) sin(n π x / L) eV or Joules Quantum & Atomic Physics

Paschen Series

The spectral series of hydrogen atom emission lines produced by electron transitions dropping from upper energy states to the n=3 level.

1 / λ = R_H (1 / 3² - 1 / n_i²), n_i = 4, 5, 6... Infrared Wavelengths (nm) Quantum & Atomic Physics

Pauli Exclusion Principle

A fundamental quantum law stating that two identical fermions cannot occupy the exact same quantum state simultaneously.

No two identical fermions can occupy the same quantum state: ψ(1,2) = -ψ(2,1) Dimensionless Quantum Law Quantum & Atomic Physics

Phosphorescence

A type of photoluminescence where absorbed energy is emitted slowly over time due to spin-forbidden quantum transitions.

τ_phosphorescence ~ 10⁻³ s to hours Seconds to Hours (Lifetime) Quantum & Atomic Physics

Photoelectric Effect

The emission of electrons from a metal surface when light of frequency above a threshold value shines upon it.

K_max = h ν - Φ = e V_stopping eV or Joules Quantum & Atomic Physics

Planck's Law & Blackbody Radiation

The foundational law describing the spectral radiance of electromagnetic radiation emitted by a blackbody in thermal equilibrium.

B_ν(T) = (2 h ν³ / c²) / (e^(h ν / (k_B T)) - 1), E = h ν W / (m²·sr·Hz) Quantum & Atomic Physics

Population Inversion

A non-equilibrium state of a quantum system where more atoms reside in a higher excited energy state than in lower energy states.

N₂ > N₁ (Excited state density > Ground state density) Dimensionless Condition Quantum & Atomic Physics

Principal Quantum Number

The primary quantum number designating the main electron shell, overall orbital size, and principal energy level of an electron in an atom.

n = 1, 2, 3, 4... Dimensionless Integer Quantum & Atomic Physics

Probability Density

The probability per unit volume of finding a quantum particle at a specific spatial position at a given time.

P(x) = |ψ(x, t)|² = ψ*(x, t) ψ(x, t) m⁻¹ (1D) or m⁻³ (3D) Quantum & Atomic Physics

Quantum Decoherence

The loss of quantum coherence where interaction between a quantum system and its macro-environment converts a quantum superposition into a…

ρ_offdiag(t) = ρ_offdiag(0) e^(-t / τ_dec) s (Decoherence Time Constant) Quantum & Atomic Physics

Quantum Dots

Nanometer-scale semiconductor crystals that trap charge carriers in all three spatial dimensions, exhibiting artificial atom quantized…

E_gap(R) = E_bulk + (ℏ² π²) / (2 m_eff R²) nm (Size), eV (Bandgap) Quantum & Atomic Physics

Quantum Electrodynamics (QED)

The relativistic quantum field theory describing how light (photons) and charged matter (electrons/positrons) interact.

L_QED = ψ̄ (i γ^μ D_μ - m) ψ - ¼ F_μν F^μν Relativistic Quantum Field Quantum & Atomic Physics

Quantum Entanglement

A quantum phenomenon in which two or more particles become interconnected such that the quantum state of each particle cannot be described…

|Ψ⟩ = (1 / √2) (|0⟩|1⟩ - |1⟩|0⟩) Dimensionless Quantum State Quantum & Atomic Physics

Quantum Harmonic Oscillator

The quantum mechanical analogue of a classical harmonic oscillator, describing a particle bound in a parabolic potential well V(x) = ½ m ω²…

E_n = (n + ½) ℏ ω, n = 0, 1, 2, 3... eV or Joules Quantum & Atomic Physics

Quantum Operators

Linear mathematical operators that act on a wave function to yield physical observables (such as position, momentum, or energy).

p̂ = -i ℏ ∇, x̂ = x, Ĥ = -(ℏ² / (2m)) ∇² + V(x) Varies by Observable Quantum & Atomic Physics

Quantum Superposition

A core principle of quantum mechanics stating that a quantum system can exist in a linear combination of multiple distinct quantum states…

|Ψ⟩ = α |0⟩ + β |1⟩, |α|² + |β|² = 1 Dimensionless State Vector Quantum & Atomic Physics

Quantum Tunneling

A quantum phenomenon where a particle passes through a potential energy barrier higher than the particle's kinetic energy.

T ≈ exp(-2 k L), k = √(2 m (V₀ - E)) / ℏ Dimensionless (Transmission Probability)