Free Particle
[latex]{\Large\[i\hbar \frac{\partial}{\partial t}\psi(x,t) = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2}\psi(x,t)\]}[/latex]
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Infinite Well
[latex]{\Large\[i\hbar \frac{\partial}{\partial t}\psi(x,t) = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2}\psi(x,t)\;\; \mathrm{BCs}=0\]}[/latex]
Finite Step
[latex]{\Large\[i\hbar \frac{\partial}{\partial t}\psi(x,t) = \left[-\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} + V(x)\right]\psi(x,t)\]}[/latex]
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This video highlights the probability wave. |
This one gives a clearer picture of the wave function itself. Note the “feedback” between the real and imaginary parts as it evolves. |