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Course material

assigned to @michaelwimmer

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• b04150cb - Extend text of QM in smooth potential

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• 052a0f1c - animation corrected

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General organization remark: I see that the docs folder is also in the repository, but that is the one generated by execute.py as far as I understand. Basically, all material (.md files, figures, etc.) should go into the src folder.

Could you please reorganize this?

Additionally, it's fine to have svgs as figures, not necessary to convert to png.

The directory docs has been removed from the repository. It is now generated locally. The figures compiled are now saved in svg format.

Front matter

• we should add authors to the lecture notes: Juan & Michael

WKB

QM in a smooth potential

• In the classical section, we should have sketches for the cases E>V(x) and E<V(x) e.g. like this: and Initially I was thinking whether we should have an animation here, but I think it's overkill.

WKB wave function

• Two small changes: in the sketch approximating the smooth potential by small steps, I would center the steps around the smooth line like that: Additionally, I would change the colors such that the line of discrete steps on the left and on the right have the same color for consistency.

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• dd0cccbd - svg format pictures and gitignore

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• 1ca7ad1a - rm docs

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• b33718c7 - ignore docs

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Connection formulas

• Is it possible to put the final connection formulas into a table? I was wondering if that improves the formatting.

Bound states

• The picture of the initial situation would fit better as a summary at the end of the section (The reader will not know what
  $\nu$
  is)
• I'm not entirely sure what is a good initial plot. I think what is important to bring across is that we are considering a situation with $V(x)>E$ for large enough x such as
• I would suggest to have for each of the subsections (each of the different cases) to have one individual, but more detailed sketch. I.e. indicating in the sketch what
  $x_1$
  and
  $x_2$
  are, and also indicating which of them depends on
  $E$
  explicitly (i.e.
  $x_2(E)$
  ).

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• 5c8de38c - Corrected plots for wkb section

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• 4e6e1be4 - correct animations landau zener and add tables wkb connection

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Tunneling

I think we should reorganize this section, and essentially revert the order.

• Change the title into "Transport"
• Start with a sketch explaining that we now deal with a problem opposite to the bound state problem, namely E>V(x) for |x| -> \infty. And that then you can define a transport problem similar to what they did in QM with tunneling:
• Then continue with the case where E>V(x) everywhere, and hence T=1. Instead of the wave packet propagation we could instead simply have a plot of the WKB stationary wavefunction (specifically, the real part of psi, not the absolute value, in order to see oscillations). There you also see how the wave length and amplitude change. Ideal would be to have a slider where one can change e.g. the potential height (maybe even from negative [dip] to positive [peak, but always staying in E>V(X)) and see how the wave function changes - like was done in "Validity of the connection formulas"
• Only then I would go to tunneling. Now you show there 2D kwant simulations I believe. I actually meant to simply do a 1D kwant simulation, and plot a 1D wave function (e.g. the real part of psi should look like that ). Maybe also there we could have a slider changing the energy/potential height?

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• 022b2e08 - split figure of classical particle into two parts
• 89b10424 - fix order of figures
• fff56d8a - text edits for section on WKB wave function

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• df7145c6 - small edits to bound state figures; separate figure to introduce concept
• df015bec - Extended the texts on connection formulas and bound states slightly

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merged