Glossary

Every term the book defines — 150 of them — with the chapter that introduced it. These are the same definitions behind the dotted-underline tooltips throughout the site, written for a reader coming from engineering rather than physics.

150 shown

angular frequency ch. 2: ω = 2π/τ, radians per second. Energy is ħω, the time-domain counterpart of p = ħk.
antisymmetric state ch. 10: Ψ(a,b) = −Ψ(b,a). Required of identical fermions. It vanishes identically if two particles occupy the same single-particle state — which is the Pauli exclusion principle — and it is exactly zero when the two particles are at the same point.
balmer series ch. 1: The hydrogen spectral lines from n = 3, 4, 5, … down to n = 2. They land in the visible, which is why they were found first.
binding energy ch. 5: How much energy must be supplied to free a bound particle: the positive number E_B with total energy E = −E_B.
black-body radiation ch. 1: Thermal radiation in equilibrium with a perfect absorber. Explaining its spectrum forced Planck in 1900 to assume atoms emit and absorb energy in discrete quanta E = hν.
bohr magneton ch. 8: μ_B = eħ/2m_e = 9.274×10⁻²⁴ J T⁻¹, the natural unit for magnetic moments associated with electrons.
bohr radius toolkit: a₀ = 4πε₀ħ²/mₑe² = 0.5292 × 10⁻¹⁰ m. The only length you can build from ħ, e, mₑ and ε₀, and it is the size of a hydrogen atom. The unit almost every atomic distance is quoted in.
born interpretation ch. 3: |Ψ(r,t)|² d³r is the probability of finding the particle in the volume d³r. Max Born, 1926 — the bridge from the Schrödinger equation to anything measurable.
bose–einstein condensate ch. 10: A macroscopic population of bosons occupying the same single-particle state, with mutually coherent wave functions that move collectively without friction. Predicted in the 1920s; the first pure condensate was made in 1995, and Cornell, Ketterle and Wieman shared the 2001 Nobel Prize for it.
boson ch. 10: A particle of integer spin. Systems of identical bosons have symmetric states, so any number may occupy one single-particle state — which is what makes laser coherence, superfluidity and Bose–Einstein condensation possible. Photons, ⁴He atoms and the deuteron are bosons.
bound state ch. 5: A state trapped near a potential well, with energy below the potential at infinity. Its energies are discrete and its wave function decays exponentially outside the well.
canonical commutation relation ch. 7: [x̂,p̂] = iħ. The single algebraic fact that forbids a state of definite position and momentum, and from which the uncertainty principle can be derived.
central field approximation ch. 11: Replacing the unsolvable Z-electron problem with Z independent one-electron problems, each in an averaged spherically symmetric potential. It is what makes atoms tractable, and Eq. (11.6) is then literally Eq. (9.5) — so every quantum number and every method from ch09 survives.
central potential ch. 9: A potential depending only on the distance from a fixed origin, V(r). It exerts no torque, so angular momentum is conserved, the eigenfunctions separate as R(r)Y_{l,m}(θ,φ), and the problem reduces to one dimension in r.
centrifugal barrier ch. 9: The l(l+1)ħ²/2mr² term in the effective potential: repulsive and singular at the origin, so it keeps every state with l > 0 away from r = 0. Only l = 0 states have appreciable density at the nucleus.
classical wave equation ch. 2: ∇²Ψ = c⁻²∂²Ψ/∂t², the equation of non-dispersive waves. Second order in time, real solutions. NOT the Schrödinger equation.
classically forbidden region ch. 5: Where E < V(x). A classical particle can never be there; a quantum one has ψ decaying as e^(−αx) and a real chance of being found.
collapse of the wave function ch. 3: The abrupt, non-deterministic replacement of a state by a new one compatible with a measured outcome. Phillips: the underlying mechanism is not understood.
commutator ch. 7: [Â,B̂] = ÂB̂ − B̂Â. It vanishes exactly when two observables are compatible, so it is the test for whether they can be known together.
compatible observables ch. 7: Two observables that can be sharply defined at the same time. Equivalently, two whose operators commute, and which therefore share a complete set of simultaneous eigenfunctions.
complete orthonormal basis ch. 4: A set of eigenfunctions that are normalized, mutually orthogonal, and sufficient to express any wave function as a superposition. The infinite-dimensional version of an orthonormal basis in linear algebra.
complete set of compatible observables ch. 7: The smallest set of mutually compatible observables whose simultaneous eigenvalues label a quantum state uniquely — one for a particle in 1-D, three in 3-D.
compton effect ch. 1: The increase in an X-ray's wavelength when it scatters off an electron, Δλ = (h/mₑc)(1−cos θ). It is exactly what you get by treating the collision as elastic between two particles.
compton wavelength ch. 1: h/mₑc = 2.43 × 10⁻¹² m. Sets the size of the Compton shift, and the floor on how precisely a particle of mass m can be located.
constant of motion ch. 7: An observable whose expectation value never changes with time, which happens exactly when its operator commutes with the Hamiltonian. Conservation laws are commutators that vanish.
de broglie wavelength ch. 1: λ = h/p — the wavelength a particle of matter behaves with. For a non-relativistic electron, λ = √(1.5/E) nm with E in eV.
degeneracy ch. 4: Several independent eigenfunctions sharing one eigenvalue. It comes from symmetry — a cubical box has it, a box with unequal sides does not — which is why breaking a symmetry splits levels.
delta-function normalization ch. 7: The condition ∫ψ*_{x′}ψ_{x″}dx = δ(x′−x″), obeyed by position and momentum eigenfunctions. They are orthogonal but cannot be normalized to 1, so neither is a physically acceptable state on its own — only superpositions of them are.
dirac delta function ch. 7: δ(x−x′): zero everywhere except x′, infinite there, with unit area. Defined by what it does inside an integral, ∫f(x)δ(x−x′)dx = f(x′), rather than by its values. The position eigenfunction.
dispersion relation ch. 2: The function ω(k). It alone decides whether a packet keeps its shape or spreads, and it is what a wave equation really encodes.
dispersive wave ch. 2: A wave whose ω(k) is not simply ck, so components travel at different speeds and packets spread. De Broglie waves are dispersive.
dissociation energy ch. 6: The depth of a molecular potential well. Above it the bound levels merge into a continuum and the harmonic approximation to the bond fails.
effective nuclear charge ch. 11: Z*e, the point charge that would produce the binding an electron actually feels. For sodium's valence electron it is 1.84e in 3s, 1.18e in 3p and 1.003e in 3d — screening increases sharply with l, because higher l penetrates the core less.
effective potential ch. 9: V_e(r) = l(l+1)ħ²/2mr² + V(r) — the true potential plus the centrifugal barrier. Radial motion behaves exactly like a one-dimensional problem in this potential, classically (Eq. 9.3) and quantum mechanically (Eq. 9.10) alike.
ehrenfest theorem ch. 3: The statement that expectation values obey the classical equations of motion: m d⟨x⟩/dt = ⟨p⟩ and d⟨p⟩/dt = −⟨dV/dx⟩. It is how the correspondence principle gets its teeth — a baseball's ⟨x⟩ moves exactly as Newton says — but it constrains only the averages, not any individual outcome.
eigenfunction ch. 4: A function an operator returns unchanged apart from a multiplying constant: Ĥψ = Eψ. The continuous analogue of an eigenvector, and the constant E is the eigenvalue.
eigenvalue toolkit: A value an observable can actually be measured to have — a solution λ of Âψ = λψ. Hermitian operators have real eigenvalues, which is exactly what lets them stand for measurement outcomes.
eigenvalue problem ch. 4: A differential equation plus boundary conditions that has solutions only for particular values of a parameter. Discretized, it is exactly the matrix eigenvalue problem you already know.
elastic constant ch. 6: The k in F = −kx, giving ω = √(k/m). For a diatomic molecule it measures the stiffness of the chemical bond, and infrared spectroscopy measures it directly.
electric dipole transition ch. 9: The most probable radiative transition, driven by the interaction −d·E with dipole operator d = −er. Its matrix element vanishes unless the two states have opposite parity, which yields the Δl = ±1 selection rule.
electron affinity ch. 11: The energy released when a neutral atom binds an extra electron — 3.5 eV for fluorine, 3.6 eV for chlorine. It is why halogens are reactive despite their high ionization energies: they gain by taking an electron, not by losing one.
electron configuration ch. 11: The list of occupied orbitals with their occupancies, such as (1s)²(2s)²(2p)² for carbon. The coarsest useful description of an atomic state — one configuration generally contains several distinct energy levels once residual repulsion is included.
electron–electron avoidance parameter ch. 11: Section 11.3's fitted f in R_ee = fR: how much better than typical the electrons are at keeping apart. f = 1.67 reproduces helium's binding energy and radius. A fitted stand-in for correlation, not a derived quantity.
electronvolt toolkit: The energy an electron gains crossing one volt: 1 eV = 1.602 × 10⁻¹⁹ J. Not a new idea, just a convenient size — it puts atomic energies in the range 1–100 instead of 10⁻¹⁹.
energy eigenvalue equation ch. 4: Ĥψ = Eψ, also called the time-independent Schrödinger equation. Solving it gives the allowed energies of a system and the spatial shapes that go with them.
energy probability amplitude ch. 4: The coefficient cₙ in that expansion. |cₙ|² is the probability that a measurement returns Eₙ — the Born rule applied to energy instead of position.
entangled state ch. 1: A joint state of two or more particles that cannot be written as a product of separate single-particle states — both particles are associated with both states at once. Introduced in ch01 for photon polarization and formalised in ch10, where it turns out that identical particles occupying different single-particle states are NECESSARILY entangled, since only an entangled combination can have definite exchange symmetry.
exchange integral ch. 10: The extra energy K that exchange symmetry contributes to an interacting identical pair: ΔE for a symmetric state is the distinguishable value plus K, and for an antisymmetric state it is minus K. Problem 3(b) derives it. The book does not name it, but it is what makes Hund's first rule and, ultimately, ferromagnetism.
exchange symmetry ch. 10: The behaviour of a state when two identical particles are swapped. Consistency of probability forces the wave function to be either unchanged (symmetric) or sign-reversed (antisymmetric) — Eq. (10.4) shows there is no third possibility.
expectation value ch. 3: ⟨x⟩, the average over infinitely many repeated measurements on identically prepared systems. Note it need not be a possible outcome at all.
fermi hole ch. 10: The region of zero probability along x_p = x_q in an antisymmetric two-particle state — two identical fermions are never found at the same point. The site uses the standard name; the book describes the effect without naming it. It is not caused by any force: the Hamiltonian of Eq. (10.7) has no interaction term, and all three states of §10.2 have the same energy.
fermion ch. 10: A particle of half-integer spin. Systems of identical fermions have antisymmetric states, so no two may share a single-particle state. Electrons, protons, neutrons, quarks and ³He atoms are fermions.
fine structure ch. 9: The splitting of hydrogen's levels at order α⁴m_ec² ≈ 10⁻⁴ eV, from the relativistic correction to the kinetic energy and the spin–orbit interaction together. It separates 2p_{3/2} from 2p_{1/2} but leaves 2s_{1/2} and 2p_{1/2} degenerate.
fine structure constant toolkit: α = e²/4πε₀ħc = 1/137.0, dimensionless. It is the electron's orbital speed in hydrogen as a fraction of c, so α² ≈ 5 × 10⁻⁵ measures how badly non-relativistic quantum mechanics is wrong.
finite difference toolkit: Replacing a derivative by a difference of neighbouring samples. The 3-point stencil [1,−2,1]/h² approximates d²/dx² to O(h²); it is the same kernel as the discrete Laplacian in image processing.
fuzzy vector ch. 8: The chapter's name for a quantum angular momentum: an object with a definite magnitude and a definite value for exactly one Cartesian component, the other two being uncertain but quantized when measured. The classical picture of a vector pointing in a definite direction has no quantum counterpart.
gamow energy ch. 5: E_G = (e²/4πε₀ħc)² 2π²μc², equal to 493 keV for two protons. It sets the Coulomb-barrier tunnelling rate T ≈ exp(−√(E_G/E)), and hence how slowly stars burn.
generalized fourier series ch. 4: Ψ = Σ cₙψₙe^(−iEₙt/ħ) — the same idea as a Fourier series, with a Hamiltonian's eigenfunctions in place of sines and cosines.
group velocity ch. 2: v_g = dω/dk — the speed of a wave packet's envelope. Requiring it to equal the particle's velocity is what fixes the Schrödinger equation.
hamiltonian toolkit: The total-energy operator Ĥ = −(ħ²/2m)d²/dx² + V(x). Discretized on a grid it is a real symmetric tridiagonal matrix, and its eigenvalues are the allowed energies.
hamiltonian operator ch. 4: Ĥ = −(ħ²/2m)∇² + V(r). It plays two roles at once: the energy observable, and the generator of time evolution — the Schrödinger equation is just iħ ∂Ψ/∂t = ĤΨ.
harmonic oscillator ch. 6: A particle in V(x) = ½mω²x², with equally spaced energy levels Eₙ = (n+½)ħω. Every smooth potential minimum looks like this when you zoom in far enough, which is why it is the most reused model in physics.
heisenberg uncertainty principle ch. 1: Δx Δp ≥ ħ/2. Not a statement about clumsy apparatus but about what simultaneously exists: there is no evidence for particles having both a definite position and a definite momentum.
hermite polynomial ch. 6: The degree-n polynomial Hₙ multiplying the Gaussian in the oscillator eigenfunction ψₙ ∝ Hₙ(x/a)e^(−x²/2a²). Its n roots are exactly the n nodes of ψₙ.
hermitian operator ch. 7: An operator obeying ∫Ψ₁*ÂΨ₂ = ∫(ÂΨ₁)*Ψ₂. This is what guarantees real eigenvalues and real expectation values — and measurements return real numbers, so every observable is described by one.
identical particles ch. 10: Particles of the same species. In classical physics they can be told apart by watching their trajectories; in quantum physics there are no trajectories, so they are genuinely indistinguishable and any labelling of them must have no physical consequence.
ionization ch. 1: Giving a bound electron enough energy to escape — above 13.6 eV for hydrogen. Beyond that the energy is no longer quantized but continuous.
ionization energy ch. 11: The energy needed to remove the least bound electron from a neutral atom. Its variation with Z is the periodic table made quantitative: 24.6 eV for helium, 5.4 eV for lithium, 21.6 eV for neon, 5.1 eV for sodium.
j–j coupling ch. 11: Couple each electron's own l and s into a j first, then combine the j's into J. Appropriate when spin–orbit coupling dominates residual repulsion, which is the case for heavy atoms.
klein-gordon equation ch. 2: The relativistic wave equation attempted in ch02 problem 6. Its solutions cannot be interpreted as wave functions; they only make sense as quantum field operators.
l–s coupling ch. 11: Combine all the electrons' orbital angular momenta into L and all their spins into S, then couple L and S into J. Appropriate when residual electron–electron repulsion is larger than spin–orbit coupling — that is, for light atoms. Also called Russell–Saunders coupling.
lamb shift ch. 9: The small further splitting of hydrogen's 2s_{1/2} from 2p_{1/2}, which fine structure leaves degenerate. It arises from the quantized electromagnetic field and lies outside this book's scope, but its existence is why the degeneracy is not exact.
landé g-factor ch. 8: The dimensionless factor g in an atom's magnetic moment, g = 1 + [j(j+1) − l(l+1) + s(s+1)]/2j(j+1). It equals 2 when the magnetism is due to electron spin alone and 1 when due to orbital motion alone.
linear operator ch. 7: An operator obeying Â(c₁Ψ₁ + c₂Ψ₂) = c₁ÂΨ₁ + c₂ÂΨ₂. Required of every observable, because otherwise the principle of superposition would not survive measurement.
lyman series ch. 1: The hydrogen spectral lines from n = 2, 3, … down to the ground state n = 1. Ultraviolet, 91–122 nm.
magnetic moment ch. 8: μ = (q/2m)L for a classical orbiting charge. In quantum physics a magnetic moment is proportional to an angular momentum and is therefore also a fuzzy vector.
matching conditions ch. 5: Continuity of ψ and dψ/dx wherever a piecewise potential steps. Joining the pieces smoothly is what selects the discrete bound-state energies — the entire technique of chapter 5.
measurement problem ch. 3: The unresolved question of how and when a quantum state stops evolving smoothly under the Schrödinger equation and abruptly collapses to one measured outcome. The theory supplies both rules but not the boundary between them, and says nothing about what counts as a measurement.
metastable state ch. 9: A state that cannot decay by electric dipole radiation, so it survives far longer than a typical excited state. Hydrogen's 2s cannot reach 1s without violating Δl = ±1, and lives 0.14 s against 2p's 1.6 ns — a factor of 10⁸.
momentum-space wave function ch. 3: Ψ̃(p,t), the Fourier transform of Ψ(x,t). It is the probability amplitude for momentum exactly as Ψ is for position.
natural line width ch. 4: The unavoidable spectral width of light from a decaying state, ΔE ≈ ħ/τ. A short-lived state has a correspondingly uncertain energy.
noble gas ch. 11: An atom whose shells close exactly — helium, neon, argon, krypton at Z = 2, 10, 18, 36. Small, tightly bound, high ionization energy, hard to excite, and almost chemically inert.
non-locality ch. 1: Measuring one member of an entangled pair fixes a property of the other however far away it is. A measurement here changes what is true there.
non-stationary state ch. 4: A superposition of different energies. Its observable properties oscillate, and the more uncertain the energy the faster they change.
normalization condition ch. 3: The requirement that the total probability is 1: ∑ₙ pₙ = 1 for discrete outcomes, ∫ρ(x) dx = 1 for a continuous one. Applied to a wave function it fixes the otherwise arbitrary overall constant, since the Schrödinger equation is linear and cannot fix it.
normalization constant ch. 3: The factor N chosen so that ∫|Ψ|²dx = 1. Fixing it is usually the first step after solving for a wave function's shape.
nuclear magneton ch. 8: μ_N = eħ/2m_p = 5.05×10⁻²⁷ J T⁻¹, the natural unit for nuclear magnetic moments — smaller than the Bohr magneton by the mass ratio m_p/m_e ≈ 1836.
observable ch. 7: A physical quantity that can be measured, represented by an operator whose eigenvalues are the possible outcomes of measuring it.
operator toolkit: A rule that takes a function and returns a function — d/dx, or "multiply by x". Written with a hat, Â. Discretize space and it becomes literally a matrix, so every question about an operator is a linear-algebra question.
orbital ch. 11: Atomic-physics name for a single-electron state in the central potential, labelled by n, l, m_l and m_s and written 1s, 2s, 2p… Each orbital holds exactly one electron. NOT the same as an orbital SHAPE, and not a classical orbit.
oscillator length ch. 6: a = √(ħ/mω), the only length a harmonic oscillator possesses. It sets the width of every eigenfunction, and ⟨x²⟩ = (n+½)a².
parity ch. 5: Whether a wave function is unchanged (even parity) or changes sign (odd parity) under reflection through the origin — x → −x in one dimension, r → −r in three. A reflection-symmetric Hamiltonian always has eigenfunctions of definite parity. For a central potential the parity is even when l is even and odd when l is odd, which is what forces the Δl = ±1 selection rule.
partial wave ch. 8: The coefficient c_{l,m_l}(r) in the spherical-harmonic expansion of a scattered wave. Each decomposes into incoming and outgoing spherical waves, and scattering shifts the phase of the outgoing one — the 3-D generalization of §5.1's phase shift.
pauli exclusion principle ch. 10: At most one fermion per single-particle state. It is not an extra postulate: a state occupied by two identical fermions would have to be symmetric under their exchange, and fermions require antisymmetric states, so such a state is identically zero.
penetration parameter ch. 5: β = √(2m(V_B − E))/ħ, the inverse decay length of a wave function inside a barrier. Its size is why tunnelling is so violently sensitive to the gap.
phase shift ch. 5: The δ in ψ = D sin(kx + δ) for a scattered wave. For fixed energy it is the only thing scattering can change, and it is what a scattering experiment actually measures.
phase velocity ch. 2: ω/k — the speed of an individual crest. For a de Broglie wave it is half the particle's speed and carries no physical meaning on its own.
photoelectric effect ch. 1: Light ejects electrons from a metal only above a threshold frequency, however intense it is — evidence that light delivers energy in hν lumps rather than continuously.
photon ch. 1: A particle-like quantum of electromagnetic radiation, carrying momentum p = h/λ and energy E = hc/λ. Light delivers its energy in these lumps, not continuously.
principal quantum number ch. 1: The integer n = 1, 2, 3, … labelling a hydrogen energy level, Eₙ = −E_R/n² = −13.6/n² eV. Chapter 9 gives it its meaning: n = n_r + l + 1, combining the radial quantum number and the orbital one — which is why levels with different l can share an energy, and why level n holds n² orbital states.
probability amplitude ch. 3: Ψ itself: the complex thing you square to get a probability. Amplitudes superpose; probabilities do not, and the difference is the interference term.
probability current ch. 3: j(x,t), obeying ∂ρ/∂t = −∂j/∂x. The flow of probability into and out of a region — the same bookkeeping as charge conservation in E&M.
probability density toolkit: |Ψ|², carrying units of 1/length in one dimension. Not a probability: only its integral over an interval is. The same object as a probability density function in statistics.
probability distribution ch. 3: The set of probabilities pₙ for the outcomes of a discrete random variable. It must sum to 1 — the statement that something happens.
quantum number ch. 3: An integer (or half-integer) labelling one of a system's discrete states — n = 1, 2, 3, … for a particle in a box. It appears because confinement admits only solutions that fit the boundary conditions, not because anything was quantized by hand.
quantum particle ch. 1: Phillips' term for an object with both particle-like and wave-like character, used to avoid implying it has a classical trajectory.
quantum state ch. 3: What a wave function represents — a state of motion bearing only a passing resemblance to a classical trajectory. In general it is a complex vector.
quasi-classical state ch. 6: A superposition of oscillator states whose |cₙ|² is Poisson-distributed about a large mean n̄. Its ⟨x⟩ traces classical simple harmonic motion, and its relative energy spread falls as 1/√n̄.
radial quantum number ch. 9: n_r = 0, 1, 2, … — the number of nodes of the radial function u(r) strictly between r = 0 and r = ∞. More radial nodes means more radial kinetic energy, hence higher energy.
radial schrödinger equation ch. 9: Eq. (9.9): the one-dimensional equation −(ħ²/2m)u″ + V_e(r)u = Eu for u(r) = rR(r), with u(0) = 0 and u(∞) = 0. The grid-plus-eigh recipe of ch00 applies to it unchanged.
raising and lowering operators ch. 6: The operators [q − d/dq] and [q + d/dq], which step a solution up or down one rung of the energy ladder. The lowering operator annihilates the ground state, and that is what makes the ladder stop.
reduced mass ch. 5: μ = m₁m₂/(m₁+m₂), the effective mass of a two-body relative motion. It turns a two-particle problem into one particle moving in the separation r; μ = m_p/2 for two protons.
residual electron–electron repulsion ch. 11: The part of the electron–electron interaction that no central potential can absorb. It splits a single configuration into several terms — carbon's (2p)² becomes ³P, ¹D and ¹S — because states of different exchange symmetry and different L keep the electrons apart to different degrees.
rydberg energy toolkit: E_R = ħ²/2mₑa₀² = ½α²mₑc² = 13.61 eV — what it costs to pull the electron off a hydrogen atom. The most quoted number in the book.
scanning tunnelling microscope ch. 5: An instrument that images single atoms by holding a metal tip under a nanometre from a surface and servoing on the tunnelling current, which changes about 2% per 0.001 nm of gap.
schrodinger equation ch. 2: iħ ∂Ψ/∂t = [−(ħ²/2m)∇² + V]Ψ. Postulated and then tested, never derived. First order in time and second in space, which forces its solutions to be complex.
schwarz inequality ch. 7: ∫|α|²∫|β|² ≥ |∫α*β|², for any two square-integrable functions. The purely mathematical step behind the uncertainty principle: with α = ÂΨ and β = B̂Ψ it becomes ⟨A²⟩⟨B²⟩ ≥ |∫Ψ*ÂB̂Ψ|². It is Cauchy–Schwarz, and it is an equality exactly when α and β are parallel — which is why the oscillator ground state saturates ΔxΔp = ħ/2.
screening ch. 11: The cancellation of part of the nuclear charge by inner electrons, so an outer electron sees an effective charge between Ze and e. Screening is what makes an orbital's energy depend on l as well as n, and therefore what breaks hydrogen's accidental degeneracy and creates chemistry.
selection rule ch. 9: A condition a transition must satisfy for its matrix element to be non-zero. For electric dipole transitions in hydrogen it is Δl = ±1 (Eq. 9.28) — a transition that violates it is not merely unlikely but forbidden at this order.
self-consistent field ch. 11: The resolution of a circularity: the central potential depends on where the electrons are, which depends on the central potential. Guess, solve, recompute the potential, repeat until the two agree. Hartree's method, and the reason atomic structure is a numerical subject.
shell ch. 11: The orbitals sharing one principal quantum number: K for n = 1, L for n = 2, M for n = 3. A closed shell is compact, tightly bound and chemically inert, which is what makes the noble gases noble.
singlet and triplet ch. 10: The two-particle spin states of two spin-halves. The triplet has S = 1 with M_S = +1, 0, −1 and is symmetric; the singlet has S = 0 and is antisymmetric. For electrons the spin symmetry then fixes the spatial symmetry, which is why the combined spin controls whether two electrons huddle or avoid.
spectroscopic notation ch. 8: The letters s, p, d, f, g labelling orbital states with l = 0, 1, 2, 3, 4, inherited from the classification of atomic spectra.
spherical harmonic ch. 8: Y_{l,m_l}(θ,φ), the simultaneous eigenfunctions of L̂² and L̂_z, satisfying L̂²Y = l(l+1)ħ²Y and L̂_zY = m_lħY. They form a complete orthonormal set of angular shapes on the sphere.
spin ch. 8: An intrinsic angular momentum carried by a point particle, with no classical analogue — it cannot be the orbital motion of constituent parts. Quantum number s, which may be half-integer; the electron has s = ½.
spin–orbit interaction ch. 9: The coupling ∝ L·S between the electron's spin magnetic moment and the magnetic field it experiences from the nucleus's apparent motion. Of order α⁴m_ec², the same size as the relativistic kinetic-energy correction, and it forces states to be labelled by j.
spin–statistics theorem ch. 10: The connection between a particle's spin and its exchange symmetry: integer spin implies symmetric states, half-integer spin implies antisymmetric ones. Pauli found it empirically in 1924 and proved it from relativistic quantum field theory some 17 years later.
standing wave ch. 2: Two counter-propagating waves superposed. It oscillates and undulates but does not travel — the shape stays put.
stationary state ch. 4: Ψ = ψ(r)e^(−iEt/ħ): definite energy, ΔE = 0, and no observable property changes with time — ever. The wave function keeps rotating in the complex plane while nothing measurable moves.
stern–gerlach experiment ch. 8: Passing atoms through a non-uniform magnetic field, so each is deflected by a force −μ_z ∂B/∂z and the beam splits into 2j+1 separate beams. Direct evidence that a Cartesian component of angular momentum is quantized; silver atoms split into two, so their ground state has j = ½.
superposition principle ch. 2: The Schrödinger equation is linear in Ψ, so any sum of solutions is a solution. This is what lets a particle be in two places at once.
symmetric state ch. 10: Ψ(a,b) = +Ψ(b,a). Required of identical bosons. Any number of bosons may share one single-particle state, and two in the same place are twice as likely as two distinguishable particles would be.
term symbol ch. 11: The label ^{2S+1}L_J: multiplicity 2S+1, a capital letter S, P, D, F for L = 0, 1, 2, 3, and total angular momentum J as a subscript. Carbon's ground term is ³P₀. CAUTION: the letter S for L = 0 is unrelated to the spin quantum number S in the superscript.
time delay ch. 5: τ = 2ħ dδ/dE — the observable meaning of a phase shift. The same quantity as group delay in a filter, and negative when a particle speeds up crossing a well.
total angular momentum ch. 8: The combination of orbital and spin angular momentum, described by quantum numbers j and m_j, where j = l+s, l+s−1, …, |l−s|.
transmission probability ch. 5: T = |A_T|²/|A_I|², the chance a particle crosses a barrier. With the reflection probability R it satisfies R + T = 1 — the only two outcomes.
tunnelling ch. 5: Transmission through a region where E < V, impossible in classical physics. The probability falls off as e^(−2βa), exponentially in both barrier width and height.
unbound state ch. 5: A state that extends to infinity, with energy above the potential there. Unbound energies form a continuum — any value is allowed — unlike the discrete bound ones.
untangled state ch. 10: The book's term for a plain product wave function such as ψ_n(x_p)ψ_n′(x_q), available only to distinguishable particles. Identical particles in different states cannot have one.
valence electron ch. 11: The loosely bound electron or electrons outside the closed shells. Chemistry is almost entirely their behaviour; the closed shells beneath simply screen the nucleus.
variance ch. 3: (Δx)² = ⟨x²⟩ − ⟨x⟩² — the average of the square minus the square of the average. Its square root Δx is the standard deviation, or uncertainty.
vibrational energy level ch. 6: An energy level of two nuclei vibrating about their equilibrium separation, spaced by ħ√(k/μ). Transitions between adjacent levels give infrared spectral lines.
virial theorem ch. 7: For a stationary state, 2⟨T⟩ = ⟨r dV/dr⟩. It gives ⟨T⟩ = ⟨V⟩ for a harmonic oscillator and 2⟨T⟩ = −⟨V⟩ for a Coulomb potential.
wave function toolkit: The complex-valued function Ψ(x,t) holding everything knowable about a particle. It is not itself observable; |Ψ|² is. Discretized on a grid, it is a complex vector.
wave number ch. 2: k = 2π/λ — spatial frequency in radians per metre. Momentum is ħk, so k is where the particle description and the wave description meet.
wave packet ch. 2: A superposition of a band of wave numbers, localized in space. Its length is about 2π/Δk, so a narrow band means a long packet.
wave-particle duality ch. 1: Particle-like properties appear on detection; wave-like properties are inferred from the statistics of many detections. Which one you can infer depends on the experiment.
well-depth parameter ch. 5: The number w defined by V₀ = ħ²w²/2m. It packages a well's depth and width into one quantity, and it alone decides how many bound states the well supports.
zeeman effect ch. 8: The splitting of spectral lines by a magnetic field: each level with quantum number j splits into 2j+1 magnetic levels, so one line becomes several closely spaced ones.
zero-point energy ch. 4: The lowest energy of a confined particle, which is never zero. Forced by the uncertainty principle: confine a particle to a length a and its momentum spread costs kinetic energy.