A particle trapped in an infinite potential well. The wave function can only exist at specific energy levels — this is quantization.

Only specific energies are allowed:

Eₙ = n²π²ℏ²/2mL²

n=1 is the ground state — lowest possible energy. The particle can never have zero energy. This is the zero-point energy.

Inside the well:

ψₙ(x) = √(2/L) sin(nπx/L)

The probability of finding the particle at position x is |ψ(x)|². Higher n = more nodes = higher energy.

A particle can exist in a superposition of energy levels. The combined wave function oscillates in time — this is quantum beating.