Physics
Schrödinger 1D
Wave packets: tunnelling, wells and energy levels.
What happens
A quantum wave packet living by the Schrodinger equation: it spreads as it flies, sloshes forever in a harmonic well, and at a barrier does what no classical ball can, splitting into a reflected part and a tunnelled one. The norm stays pinned at one: probability is never lost.
Equations used in the module
Equations iħ ∂ψ/∂t = −(ħ²/2m) ∂²ψ/∂x² + V ψ T ≈ exp(−2 ∫ √(2m(V − E)) dx / ħ) (tunnelling) E_n = n² π² ħ² / (2 m L²) (box)
