Quantum Mechanics I - Vocabulary Flashcards

Vocabulary-style flashcards covering key terms from quantum mechanics, wavefunctions, operators, and spectroscopy topics in the notes.

Blackbody radiation

Electromagnetic energy emitted by an ideal object that absorbs all radiation; emission depends only on temperature; classical physics predicts the ultraviolet catastrophe.

Ultraviolet catastrophe

Classical prediction of infinite energy at very short wavelengths for blackbody radiation.

Planck's quantization of energy

Energy is emitted or absorbed in discrete units (quanta) E = hν for each oscillator, solving the ultraviolet catastrophe.

Planck's constant

Fundamental constant h relating energy and frequency (E = hν); h ≈ 6.626×10^-34 J·s.

De Broglie wavelength

Wavelength associated with a particle of momentum p, given by λ = h/p (λ = h/(mv) for nonrelativistic particles).

Wave–particle duality

Idea that particles exhibit both wave-like and particle-like properties.

Double-slit experiment

Experiment showing interference for particles when not observed, and particle-like behavior when measured.

Wavefunction

ψ(x,t): mathematical description of a quantum system containing probability amplitudes; must be normalized.

Schrödinger equation

Fundamental equation of quantum mechanics; time-dependent form governs evolution of ψ; time-independent form yields energy eigenvalues.

Hermitian operator

Operator associated with a measurable quantity; has real eigenvalues and, if commuting, shares eigenfunctions.

Eigenvalue

Possible value obtained when measuring an observable corresponding to an eigenfunction: Âψ = aψ.

Eigenfunction

Nonzero function ψ that satisfies Âψ = aψ for some eigenvalue a.

Expectation value

Average value of an observable in a given state: ⟨A⟩ = ∫ ψ* A ψ dx.

Normalization

Process ensuring total probability equals 1; ∫ |ψ|^2 dx = 1.

Orthogonality

Different eigenfunctions are orthogonal: ∫ ψi* ψj dx = 0 for i ≠ j.

Born interpretation

Probability density of finding a particle at x is |ψ(x)|^2; integrated over a region gives the probability.

Heisenberg uncertainty principle

Δx Δp ≥ ħ/2; improving precision in position reduces precision in momentum, and vice versa.

Pauli exclusion principle

For fermions, the total wavefunction must be antisymmetric; no two fermions can occupy the same quantum state.

Time-dependent Schrödinger equation

iħ ∂ψ/∂t = Ĥψ; describes the time evolution of the wavefunction.

Particle in a box

1D model with zero potential inside 0 < x < L and infinite walls; allowed states are sine functions with En ∝ n^2.

Free particle

Particle with no potential; energy is purely kinetic and not quantized; plane-wave solutions.

Rigid rotor

Model of rotational motion with fixed bond length; discrete rotational energy levels depending on moment of inertia.

Harmonic oscillator

System with restoring force proportional to displacement; equally spaced energy levels; solutions involve Hermite polynomials and Gaussian factors.

Bohr radius

Characteristic length a0 = 4π ε0 ħ^2 / (m e^2) ≈ 0.529 Å; scale for hydrogenic systems.

Rydberg equation

Relation for hydrogen spectral lines: 1/λ = R_H (1/n1^2 − 1/n2^2); n1 < n2.

Hydrogenic atom

One-electron atoms or ions (e.g., H, He^+, Li^2+, etc.) that resemble hydrogenic energy levels.

Born-Oppenheimer approximation

Nuclei move much more slowly than electrons; solve electronic structure with fixed nuclei, then treat nuclear motion.

Partition function

Sum over Boltzmann factors of all microstates: q = Σi e^(−βEi); β = 1/(k_B T).

Boltzmann distribution

Probability of a microstate with energy Ei: Pi = e^(−βE_i) / q.

Microstate

A distinct microscopic arrangement of a system with a specific energy.

Macrostate

Macroscopic state described by bulk properties; contains many microstates.

Multiplicity

Number of microstates corresponding to a given macrostate.

Infrared spectroscopy

Probes vibrational transitions via IR absorption; requires change in dipole moment; active for polar molecules.

Raman spectroscopy

Probes vibrational transitions via inelastic scattering; depends on change in polarizability; active for many molecules, including nonpolar ones.

Normal modes

Independent vibrational patterns of a molecule; for nonlinear molecules, 3N−6 modes; for linear, 3N−5.

CO₂ vibrational modes

Symmetric stretch (IR inactive, Raman active), asymmetric stretch (IR active), bending (IR active).

Translational motion

Linear movement of molecules through space; not usually detected in spectroscopy; includes diffusion.

One-electron atom

Atoms or ions with a single valence electron (e.g., hydrogen, He^+).

Electron–electron repulsion

Coulomb repulsion between electrons in many-electron atoms; complicates energy levels beyond hydrogenic models.

Spherical harmonics

Angular part of the wavefunction in rotational problems; appear in solutions for angular momentum and hydrogenic systems.