I am currently working on trying to understand some of the details in quantum physics.(adsbygoogle = window.adsbygoogle || []).push({});

So far, Schrodinger's equation and wave mechanics seems to provide (at least when imposing semiclassical E-M interactions with an E-M field) a decent mechanism for why electrons end up in stationary states represented by the eigenfunctions of the wave equation. (These are the ones for which the wavefunction is not accelerating, thus not disturbing the E-M field.)

I have looked through second quantization, but haven't seen any mechanism there for quantizing photons. It's sort of asserted in the axioms of setting it up.

I've seen in it stated in several places that when particles interact, they always end up in an eigenfunction of some given operator. In general, I don't see the mechanism which would cause this. First, it seems the operators are arbitrarily chosen.

In the case of electrons, if you ping a bound electron with another electron, the other electron will eventually end up in some sort of stationary state by radiation (and eventually, the ground state). But if you have some generic particle that doesn't have a mechanism for dissipating excess energy, it doesn't seem like there should be any reason that it ends up in a stationary state versus some arbitrary time-varying state.

PS - for arbitrary time-varying states, it seems like the eigenfunctions are just some arbitrary basis to decompose them into. What is special about the eigenfunctions?

I've got a model I'm playing with now, with imaginary 1d particle A that is bound in a harmonic oscillator, and imaginary 1d particle B, that starts at one end of the domain and travels as a wave packet. There is some potential between them, so they interact when they "collide", and you end up with a wave for B that either propagates through (associated with one relative state for A), or reflects, associated with another relative state for A. But A, it seems, has no preference as to where it ends up, whether eigenvalue or not.

You have to come up with some specification for B's state anyway, before you get A's state. And you can specify whatever you want for B, for greater or lesser portions of the amplitude. Am I supposed to be seeing large amounts of the amplitude associated with eigenvectors?

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# Why Eigenvectors/Eigenvalues?

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