Solution of the Schrödinger Equation in One Dimension

Abstract

The simple structure of the Schrödinger equation allows a particular ansatz in which the time and space dependences occur in separate factors,

$${\psi _E}\left( {x,t} \right) = \exp \left( { - \frac{i}{\hbar }Et} \right){\varphi _E}\left( x \right).$$