We know that not all quantum systems are quantized. For example, the free particle has a continuous spectrum of momenta. Fun question of the day: If you had to sum up in one phrase when a particles observables become quantized, what would it be? My answer: Compactness.
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But isn’t that just a necessary condition for normalization? Thanks for sharing these nice stuff
Ah, I see what you’re saying. We usually say that it’s imposing the wave function not blow up at infinity is a condition for normalizABILITY.. that is the wave function must live in some Hilbert space
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I was going to say "finite boundary conditions" as a more descriptive alternative to what I assumed you meant by comoactness. Just apply periodic ones to the atom and you get your radial solutions.
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What do you mean by periodicity in the radial solutions?
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