Particle in a Box
A elementary quantum model describing a particle trapped inside a 1D rigid box with impenetrable potential barriers (infinite potential well).
Governing formula
E_n = (n² π² ℏ²) / (2 m L²), ψ_n(x) = √(2/L) sin(n π x / L)
SI unit
eV or Joules
In depth
Boundary conditions requiring the wave function to vanish at the box walls (ψ=0 at x=0 and x=L) force standing wave solutions, yielding quantized energy levels proportional to n² and demonstrating zero-point energy (E₁ > 0).
Examples in the real world
Modeling conjugated pi-electron energy levels in organic dye molecules and semiconductor quantum wells.