Perturbation Theory Applied to Cloud Chamber Tracks

I found a scattering/perturbation theory analysis in David Park's Introduction to the Quantum Theory. I should explain that when I began these web pages I knew what perturbation theory was in this sense:

(Me, circa 2004 autumn): Perturbation theory is a method in performing calculations in quantum mechanics which starts with a known situation and then assumes that an unknown situation can be treated as the known situation plus some small changes. And beyond that vague definition I have no idea how it works.

The calculation in Park discusses the energy transfer between an alpha particle moving through a cloud chamber and a resident atom of hydrogen that happens to get in the way. So the hydrogen atom consists of a proton which is ignored and an electron which can be clobbered by the alpha particle. In the way a can of soda can get clobbered by a bus, to choose a classical analogy based on rest mass.

Now I decided to try and follow the perturbation theory calculation thinking I would pick up some ideas on how it works in the process. This worked beautifully, but for the fact that I didn't get all the way through the analysis. So it still needs to be finished. Now about a year later I can see that my work on learning quantum mechanics will eventually permit me to do a good job explaining the entire calculation. But I'm not there yet, so I'll let the earlier writeup stand for now.

There are two objectives to Park's alpha particle analysis:
1. Show that truck keeps going.
The alpha particle will tend to continue in the direction it was originally headed but with a little less energy after it knocks the electron away (say ionization, Rydberg of energy, 13.6eV).
2. Accomplish the first objective using wave mechanics and a steady-state picture.

My further objectives, unrealized, are:
1. Connect the theory to what we see in the chamber.
Calculate more numbers for the process: How long the alpha should travel before hitting an electron, how many electrons we can expect it to dislodge, how long the track should therefore be, what the alpha particle's velocity profile should look like.
2. Understand how the calculation works in the broader context of perturbation theory.

An interesting aspect of Park's derivation is that it uses the time-independent strange, strange since what we're thinking about is precisely an event in which something changes over time. 
My original notes on Park's derivation are here.

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