physics2u
Tier
⌕ Search ⌘K
physics2u.com/units/PU-202.html
Unit · year 2 · live

PU-202 · Quantum Mechanics I

Threads chance · waves · energy Lectures 32 Derivations homed 6

Wavefunctions, operators and measurement — building the machinery that replaces trajectories with amplitudes.

PREREQUISITES

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

D-007

The continuity equation & probability current

Where probability goes when it moves — the local conservation law behind normalisation.

D-008

Ehrenfest’s theorem & the classical limit

How expectation values recover Newton, and precisely when that recovery is trustworthy.

D-009

The generalised uncertainty relation

From the Cauchy–Schwarz inequality to a bound on any pair of non-commuting observables.

D-010

Oscillator spectrum by ladder operators

The algebra of raising and lowering that hands you the entire spectrum without a single integral.

D-011

Transmission through a rectangular barrier

Matching solutions across a classically forbidden region to read off the tunnelling coefficient.

D-012

Spreading of a free Gaussian wave packet

Why a localised particle refuses to stay localised, worked out from the free propagator.