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plotting wave functions and densities

One can learn a lot about a quantum system by inspecting a plot of its single-particle orbitals. In this video, you learn how single-particle orbitals (wave functions) and their corresponding densities can be visualized.

Here is an exercise about this plotting. The explicit expression for the wave function of the 2px orbital of the hydrogen atom is: ax*exp(-r/2) (‘a’ is a constant, take it to be 1). The expression for the density of this orbital is the square of it (you can look up the full expressions here).

Go here for an animated plot of the wave function and here for an animated plot of the density for this orbital. These plots are actually videos, which help you to see the wave function and density “in four dimensions”. Make sure you understand how this explicit expression gives rise to all the plots you see.

Once you understand that, it will be straightforward to make the following graphs yourself:

  • A graph with on the horizontal axis the distance to the origin, and on the vertical axis the wave function (1) along the x-axis and (2) along the y=x axis (plot both on the same graph).
  • A similar graph, but now for the density along the same two directions.

Finally, use your graph of the density to explain why you see on the animation for the density at that website two isolated spheres for sufficiently high density values.

plotting wave functions and densities

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