Quantum & Atomic Physics — 60 Terms Defined

Hydrogen Spectrum Quantum & Atomic Physics m⁻¹ (Wavenumber) The set of discrete electromagnetic emission and absorption lines produced when the electron in a hydrogen atom transitions between energy levels. 1 / λ = R_H (1 / n_f² - 1 / n_i²)

Hyperfine Structure Quantum & Atomic Physics eV or MHz (Small Energy Splitting) Extremely small energy level splittings in atoms caused by interaction between nuclear magnetic moments and electron magnetic fields. ΔE_HFS ∝ I_nucleus · J_electron

Lamb Shift Quantum & Atomic Physics MHz or eV 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)

Laser Cooling Quantum & Atomic Physics μK or nK (Temperature) 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)

Lyman Series Quantum & Atomic Physics Ultraviolet Wavelengths (nm) 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...

Moseley's Law Quantum & Atomic Physics Hz^(1/2) (Frequency Square Root) An empirical law establishing a linear relationship between the square root of characteristic X-ray frequency emitted by an atom and its atomic number Z. √ν = A (Z - b)

Orbital Angular Momentum Quantum & Atomic Physics J·s (Angular Momentum Units) 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

Particle in a Box Quantum & Atomic Physics eV or Joules A elementary quantum model describing a particle trapped inside a 1D rigid box with impenetrable potential barriers (infinite potential well). E_n = (n² π² ℏ²) / (2 m L²), ψ_n(x) = √(2/L) sin(n π x / L)

Paschen Series Quantum & Atomic Physics Infrared Wavelengths (nm) 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...

Pauli Exclusion Principle Quantum & Atomic Physics Dimensionless Quantum Law 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)

Phosphorescence Quantum & Atomic Physics Seconds to Hours (Lifetime) 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

Photoelectric Effect Quantum & Atomic Physics eV or Joules 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

Planck's Law & Blackbody Radiation Quantum & Atomic Physics W / (m²·sr·Hz) 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

Population Inversion Quantum & Atomic Physics Dimensionless Condition 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)

Principal Quantum Number Quantum & Atomic Physics Dimensionless Integer 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...

Probability Density Quantum & Atomic Physics m⁻¹ (1D) or m⁻³ (3D) 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)

Quantum Decoherence Quantum & Atomic Physics s (Decoherence Time Constant) The loss of quantum coherence where interaction between a quantum system and its macro-environment converts a quantum superposition into a classical probabilistic mixture. ρ_offdiag(t) = ρ_offdiag(0) e^(-t / τ_dec)

Quantum Dots Quantum & Atomic Physics nm (Size), eV (Bandgap) Nanometer-scale semiconductor crystals that trap charge carriers in all three spatial dimensions, exhibiting artificial atom quantized energy spectra. E_gap(R) = E_bulk + (ℏ² π²) / (2 m_eff R²)

Quantum Electrodynamics (QED) Quantum & Atomic Physics Relativistic Quantum Field 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

Quantum Entanglement Quantum & Atomic Physics Dimensionless Quantum State A quantum phenomenon in which two or more particles become interconnected such that the quantum state of each particle cannot be described independently of the others. |Ψ⟩ = (1 / √2) (|0⟩|1⟩ - |1⟩|0⟩)

Quantum Harmonic Oscillator Quantum & Atomic Physics eV or Joules The quantum mechanical analogue of a classical harmonic oscillator, describing a particle bound in a parabolic potential well V(x) = ½ m ω² x². E_n = (n + ½) ℏ ω, n = 0, 1, 2, 3...

Quantum Operators Quantum & Atomic Physics Varies by Observable 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)

Quantum Superposition Quantum & Atomic Physics Dimensionless State Vector A core principle of quantum mechanics stating that a quantum system can exist in a linear combination of multiple distinct quantum states simultaneously until measured. |Ψ⟩ = α |0⟩ + β |1⟩, |α|² + |β|² = 1

Quantum Tunneling Quantum & Atomic Physics Dimensionless (Transmission Probability) 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