Here is an electron in a wave-packet state that is a superposition of free-electron energy-eigenstate wave-functions and their time dependence. The smooth line shows the wave-function squared (in units of \(nm^{-1}\) and the oscillating curves, there are two of them, show the real and imaginary parts of the wave-function in units of \(nm^{-1/2}\). Although it says crystal wave-packet, it is actually a free-electron wave-packet (I think you can tell from the smoothness of the wave-function squared, which would be textured by the crystal lattice potential in a crystal.) This is calculated from the Schrodinger equation and a superposition of free electron eigenstates just like you are doing in HW5. I think if you plot your results it will look pretty much like this.
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Midterm 2 solutions
Here are solutions to midterm 2. I see that I did not write it in the solutions, but it is helpful for sp2 type integrals to recall that \(\...

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I am thinking that the HW this week is not so excessively long as last week's assignment. This week's HW has a problem involving a t...
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For tomorrow's class we will start a new topic, which is free particle propagation and scattering. This involves non-local states.
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Solutions below. Homework 8 includes spin problems and problems using spin matrices. Basically, what are called two level systems.
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