PROJECT / QUANTUM MECHANICS LAB

SCHRÖDINGER EQUATION

iħ∂Ψ∂t = −ħ²2m∂²Ψ∂x² + VΨ

InputPotential V(x), particle mass m, boundary conditions

SolverFinite-difference Hamiltonian, exact diagonalisation, spectral time evolution

OutputWave function ψ(x,t), probability density |ψ|², energy eigenvalues

Potential V(x)

Preset

V(x) =

Use x, + − * / ^, sin cos exp abs sqrt tanh, step(u) (1 when u ≥ 0), PI. Press Enter to solve.

Particle and domain

Mass m

Domain: x from −L to L

Grid points

Boundary conditions Hard wallsψ = 0 at both ends Reflectingdψ/dx = 0 at both ends Periodicright end wraps to the left end

Initial state ψ(x, 0)

Shape

Centre x₀

Width σ

Momentum k₀

Display

3D view

Surface height

Time shown on the surface

Speed 1×

Rotate the camera slowly

Probability density |ψ(x, t)|² on the potential

n	Eₙ	Share of the state

Lowest ten shown. Click a row to start from that eigenstate. Units: ħ and m as entered; with ħ = m = 1 energy is in units of ħ²/(m·length²).