# Definition:Schrödinger's Equation/Time Independent

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## Definition

- $-\dfrac {\hbar^2} {2 m} \nabla^2 \psi + V \psi = E \psi$

where:

- $\psi$ is the wave function whose nature is to be determined
- $V$ denotes the potential energy (usually positional)
- $E$ denotes the total energy of the system
- $m$ denotes the mass of the particle whose motion is described by $\psi$
- $\hbar$ is Planck's reduced constant:
- $\hbar = \dfrac h {2 \pi}$

## Also known as

**Schrödinger's equation** can be seen referred to as **Schrödinger's wave equation** by some authors.

## Also see

- Results about
**Schrödinger's equation**can be found**here**.

## Source of Name

This entry was named for Erwin Rudolf Josef Alexander Schrödinger.

## Sources

- 1970: George Arfken:
*Mathematical Methods for Physicists*(2nd ed.) ... (previous) ... (next): Introduction: Quantum Mechanics