Series
20 posts
Kicking off 2nd semester QM by turning the classical angular momentum L = r × p into a proper quantum operator using our existing momentum operator tools.
An intuitive introduction to intrinsic spin, spin-1/2 states, Pauli matrices, measurement probabilities, and the spin-1 representation.
How a spin-1/2 magnetic moment precesses in a uniform magnetic field, and how a field gradient separates a silver-atom beam into two Stern-Gerlach components.
How two spin-1/2 angular momenta combine into a spin-1 triplet and a spin-0 singlet, with coupled and uncoupled bases, ladder operators, and Clebsch-Gordan coefficients.
A casual walkthrough of how to read Clebsch-Gordan coefficient tables — because thankfully some genius already worked out all those messy spin-coupling combos for us.
Chapter 5 kicks off with identical particles — turns out in QM you literally can't tell two electrons apart, and that changes everything about how we write wave functions!
A friendly derivation of nondegenerate and degenerate time-independent perturbation theory, from first- and second-order corrections to the splitting of degenerate energy levels.
Working through the virial theorem proof step by step before tackling hydrogen's fine structure — commutators, expectation values, and all.
Proving ⟨1/r³⟩ for the hydrogen atom using Kramers' relation — brutal-looking but apparently the least painful option, thanks Uncle Griffiths T_T
We're back to hydrogen again?! Using perturbation theory, we dig into fine structure — relativistic corrections, spin-orbit coupling, and the Lamb shift.
We flip to the electron's frame, crank through Biot-Savart and magnetic moments, and nail down the spin-orbit Hamiltonian correction behind hydrogen's fine structure.
Working through classic perturbation theory homework problems — delta-function bumps in infinite square wells and harmonic oscillator perturbations, step by step.
A walkthrough of Griffiths Problem 6.31, deriving the weak van der Waals attraction between two polarizable atoms using perturbation theory and Taylor series.
The variational principle is basically quantum gambling — guess a trial wavefunction, and your calculated energy is always ≥ the true ground state energy.
Ch8 is all about WKB — the go-to approximation when V(x) varies slowly, letting you tackle bound states and tunneling without solving Schrödinger exactly.
At an isolated simple turning point, a local Airy solution and asymptotic matching connect the allowed and forbidden WKB regions.
Three worked WKB quantization problems: the two-turning-point condition, the harmonic oscillator and half-oscillator, and the radial logarithmic potential.
Solve a two-state delta pulse, derive multilevel transition amplitudes, and calculate excitation by a temporary potential in half an infinite square well.
Understand Planck's constant through blackbody radiation, photon energy, and the photoelectric effect, with a report, diagrams, and presentation slides.
Why don't electrons simply stop when a metal cools? Pauli exclusion explains Fermi filling, while weaker lattice scattering explains a common drop in resistivity.