Introductory Quantum Mechanics — States, Spins & Bound States
Courses
The on-ramp everything else assumes. Five postulates made concrete on the smallest systems that have any physics in them: a two-state spin, a particle in a box, a driven two-level atom. Every unit pairs the ideas with problems you solve by hand — the spectra, splittings, and pulse timings come out as real numbers you can check against experiments. Finish here and the quantum chemistry series starts on familiar ground.
States, amplitudes & measurement
● you are here0/1The five postulates, made concrete on two states: amplitudes, the Born rule, Hermitian observables, collapse, and the uncertainty relation as checkable arithmetic.
- readingReading — States, Operators & Measurement20m
- lessonAmplitudes vs probabilities: what the phase buysplanned
- lessonMeasurement as projection: order mattersplanned
Bound states in one dimension
0/4Confinement quantizes: the box spectrum from boundary conditions alone, the harmonic oscillator on a grid, and the scaling law E ∝ 1/mL² that runs from dye molecules to nuclei.
- readingReading — The Infinite Square Well15m
- exercisesExercises — The Particle in a Box by Hand50m
- readingReading — The Harmonic Oscillator on a Grid15m
- readingReading — Single-Particle Models15m
- lessonTunneling: finite walls leakplanned
Two-level systems & spin-1/2
0/4The workhorse model: one 2×2 diagonalization explains avoided crossings, the ammonia maser, Larmor precession, Rabi flopping, and magnetic quenching of positronium.
- readingReading — Two-Level Systems & Spin-1/225m
- exercisesExercises — Two-Level Systems by Hand60m
- readingWorked ladder — Spin operators in positronium (rungs 0-5)50m
- readingReading — Positronium: para, ortho & the Zeeman effect25m
- lessonThe Bloch sphere: every qubit state is a directionplanned
Angular momentum & hydrogen
0/1Why angular momentum comes in half-integer rungs, where degeneracy comes from, and the one atom solved exactly — the template every orbital picture traces back to.
- lessonLadder operators: the spectrum from algebra aloneplanned
- lessonHydrogen: the n² degeneracy and the real orbitalsplanned
- readingReading — Slater Orbitals (hydrogenic shapes)15m
- exercisesExercises — Angular Momentum by Handplanned
Time evolution
plannedStationary states do nothing; superpositions do everything. Phases, beats, wavepackets, and why the splitting frequency is the oscillation frequency.
- lessonStationary states and the phase that hidesplanned
- lessonWavepackets: motion from superpositionplanned
- exercisesExercises — Time Evolution by Handplanned
Light & matter
0/2How photons grab atoms: the dipole operator, selection rules as vanishing integrals, and oscillator strengths as the brightness bookkeeping of every spectrum.
- readingReading — The Dipole Operator & Transition Moments20m
- readingReading — Oscillator Strengths20m
- lessonSelection rules: symmetry kills integralsplanned
Toward many particles
0/2The bridge out: identical particles, the variational principle, and the first taste of why many-electron problems need the entire quantum chemistry series.
- readingReading — The Variational Principle15m
- readingReading — Many-Electron Wavefunctions20m
- lessonIdentical particles: the sign that builds the periodic tableplanned