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Thanks, Edwin. Your feedback is very much appreciated. It's funny but the electronic oscillator circuit is the example that always comes to mind for me when people say, for example, that spontaneous emission is impossible in the semi-classical approach because there is nothing to kick the process off. I mean, we would have this transistor with a couple of resistors and capacitors, and you'd draw out the circuit and by all appearances it should just sit there; and then you connect the battery and the little speaker starts to squeal. Yes, once it's squealing you can trace it around the circuit and see that it's self-sustaing. It still took a while to decide that you're not responsible for understanding how the oscillation got started in the first place.
In general I find the math hard, but even so I've done the odd calculation successfully. The crystal radio is an awesome calculation. I generally take advantage of tricks and short-cuts, so I'm not getting an exact analytical solution but I'm getting pretty good numerical results. Sometimes I can check them against the theory. If I can get a good physical visualisation of what's happening, I can usually pull out some kind of ballpark figure for it.