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Saturday, April 4, 2015

Exploring Quantum Physics - Week 1 Question 3

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.

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