PU-202 · Quantum Mechanics I
Wavefunctions, operators and measurement — building the machinery that replaces trajectories with amplitudes.
PU-201 · Classical Mechanics & PU-105 · Waves and Oscillations
You should be fluent with the Lagrangian/Hamiltonian picture and with the mathematics of standing and travelling waves. The oscillator here leans directly on D-018 · the classical harmonic oscillator from PU-201.
Lectures
| L24 |
The harmonic oscillator by ladder operators
cites D-010
|
28 min |
| L29 |
The uncertainty principle, properly
cites D-009
|
24 min |
| L18 |
Probability current & the continuity equation
cites D-007
|
21 min |
| L31 |
Tunnelling through a barrier
cites D-011
|
26 min |
Derivations homed in this unit
The continuity equation & probability current
Where probability goes when it moves — the local conservation law behind normalisation.
Ehrenfest’s theorem & the classical limit
How expectation values recover Newton, and precisely when that recovery is trustworthy.
The generalised uncertainty relation
From the Cauchy–Schwarz inequality to a bound on any pair of non-commuting observables.
Oscillator spectrum by ladder operators
The algebra of raising and lowering that hands you the entire spectrum without a single integral.
Transmission through a rectangular barrier
Matching solutions across a classically forbidden region to read off the tunnelling coefficient.
Spreading of a free Gaussian wave packet
Why a localised particle refuses to stay localised, worked out from the free propagator.