Problem:
What is the time-dependent Schrödinger equation for a particle in a potential $ V = \frac{1}{2}m\omega^2x^2 $ ?
Solution:
The Schrödinger equation with potential energy is summarized as:
$ i \hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2 \nabla^2}{2m}\psi + \frac{1}{2}m\omega^2x^2\psi $.
Note the potential energy term also have to multiply the wave function.
What is the time-dependent Schrödinger equation for a particle in a potential $ V = \frac{1}{2}m\omega^2x^2 $ ?
Solution:
The Schrödinger equation with potential energy is summarized as:
$ i \hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2 \nabla^2}{2m}\psi + \frac{1}{2}m\omega^2x^2\psi $.
Note the potential energy term also have to multiply the wave function.
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