Schrödinger Equation

The Schrödinger equation is the equation of motion for a non-relativistic quantum state. The time-dependent form says how the wavefunction evolves; the time-independent form is the energy eigenvalue problem for a static Hamiltonian.

Erwin Schrödinger published the wave equation in 1926. The most general statement uses the Hamiltonian operator $\hat{H}$ and a state $\Psi$. When $\hat{H}$ does not depend explicitly on time, stationary states satisfy $\hat{H}\psi = E\psi$.

This entry stays with the abstract operator forms. A later expression can expand $\hat{H}$ in position space as $-\frac{\hbar^2}{2m}\nabla^2 + V$.