The Schrödinger equation

Statement

$i\hbar\,\partial_t\psi = \hat{H}\psi = -\dfrac{\hbar^2}{2m}\nabla^2\psi + V\psi$ — the fundamental equation describing the time evolution of the quantum wavefunction $\psi$.

Why is it true?

Plays the role of Newton's second law but for the quantum world: knowing $\psi$ at one instant and the potential $V$, the equation tells you what $\psi$ will be at a later instant.

Topics that use this theorem

Related theorems

Step-by-step proofs

No step-by-step proof yet for this theorem.