SCHRÖDINGER 1D WELL

Quantum Bound States & Wavefunctions

The time-independent Schrödinger equation Hψ = Eψ describes quantum bound states. Each energy level has a wavefunction ψₙ(x) that oscillates with n−1 nodes. Probability density |ψ|² shows where the particle is most likely to be found.

POTENTIAL TYPE

Well Width 5.0 Well Depth / Strength 20.0 Show level n 1

Science: Quantization arises from boundary conditions. Only certain energies allow ψ→0 at walls. Harmonic oscillator gives equally spaced levels; square wells give quadratic spacing (∝n²).