The **Schrödinger equation** is a partial differential equation whose solution is the wave equation, which describes the probability density of a given particle over space. The general form of the Schrödinger equation is

where *i* is the imaginary unit, *ħ* is the reduced Planck constant, *Ψ* is the wave function, and *Ĥ* is the Hamiltonian operator (representing the total energy of the system).
In steady-state systems (where the wave equation does not depend on time, such as in an atomic or molecular orbital) this simplifies to

where *E* is a constant. This is known as the time-independent Schrödinger equation.