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Stationary states

From the previous section we observe that for systems for which the potential energy itself does not depend on time, the modulus square of the wave function \begin{eqnarray*}
\Psi(x,t) & &
\end{eqnarray*} given by

\vert\Psi(x,t)\vert^{2} & = & \Psi^{*}(x,t) \Psi(x,t) \\
& = & \vert\psi(x)\vert^{2}

Thus the probability density is independent of time. The state of the system represented by

\Psi(x,t) & = & \psi(x)\times e^{-iEt/\hbar }

is called a stationary state.

Abhijit Poddar