This application simulates the propagation of a particle's wave function by potentials like

• Step potential
• Potential barrier
• Well of Potential
• Harmonic oscillator

The initial wave function is a Gaussian packet:

$$ \Psi(x, t) = A exp\left[ \left(\dfrac{x - ⟨x⟩}{2\sigma}\right)^2 \right]e^{-iEt/\hslash} $$

The evolution of the wave function is calculated numerically from the propagator:

$$ \hat{U}(t; t_0) = e^{-i\hat{H}(t-t_0)/\hslash} $$