Schrodinger's Sandbox

Quantum Wave Functions Simulator

The Schrodinger equation

\[ i\hbar \frac{\partial \Psi}{\partial t} = -\frac{\hbar^2}{2m} \frac{\partial^2\Psi}{\partial x^2} + V \Psi \]

The potential energy function:
\( V(x) = \)

\frac{1}{2}x^2 \(x \in [ \) , \( ] \)

(After solutions appear, move the slider to see different standing wave functions!)

The initial wave function:
\( \psi(x) = \)

4 - \frac{(x+4)^2}{4} \(x \in [ \) , \( ] \)

(It will be normalized automatically)

t =
(animation speed: dt = )