The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is also often called the Schrödinger wave equation, and is a partial differential equation that describes how the wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical viewpoint, sometimes known as the Heisenberg picture.

The time-dependent one-dimensional Schrödinger equation is given by

(1)

where i is the imaginary unit, is the time-dependent wavefunction, is h-bar, V(x) is the potential, and is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts using separation of variables to write

(2)

thus obtaining

(3)

Setting each part equal to a constant then gives

			(4)
			(5)

(6)

Dirac Equation, Finite Square Potential Well, Half-Infinite Square Potential Well, Hydrogen Atom, Infinite Square Potential Well, Potential Step, Quantum Mechanics, Schrödinger Picture, Simple Harmonic Oscillator--Quantum Mechanical, Spherical Potential Well, Wave Mechanics