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.
-
But isn’t that just a necessary condition for normalization? Thanks for sharing these nice stuff
But this is true for all particles.. And imposing this is nothing special to the hydrogen atom, and usually doesn’t lead to quantization. We impose this same condition on the SHO, but that doesn’t quantize the energy
-
-
I agree that there doesn’t seem to be any intuitive way to get quantization from normalizability,but if go back to the mathematical details U’ll see that the only way to get a normalizable solution is when the series terminate and that requires Ur parameters to pick certain...
-
values. As a result, Ur energy will be quantized, I also mentioned the HO because the range is (-inf,inf) and still U get quantized parameters( unlike the H atom where U have periodicity)
End of conversation
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.