Schrodinger Equation

see also:

• Fundamental Partial Differential Equations

The Schrödinger equation is fundamental to quantum mechanics, describing how the quantum state of a physical system changes over time. It is a first-order PDE in time, but involves second-order spatial derivatives:

$i\hslash \frac{\partial \psi }{\partial t}=-\frac{{\hslash }^2}{2m}{\nabla }^2\psi +V\psi$

where $\psi$ is the wave function of the system, $\hslash$ is the reduced Planck constant, $m$ is the mass, and $V$ represents the potential energy.