Talk:Creation and annihilation operators

Energy levels

Sorry for deleting your comments about changing energy levels. I'm not familiar with quantum chemistry, only quantum field theory. Phys 22:57, 3 Apr 2005 (UTC)

Hey, no sweat – it's Wikipedia – good changes are always welcome ;) HappyCamper 23:29, 3 Apr 2005 (UTC)

| > versus |0>

So I edited the last section replacing | > with |0> before I read the section above explaining the need for the distinction. However, after reading that bit I still don't understand the distinction. It seems it would be important only if you had a infinite (-∞, ∞) versus semi-infinite [constant, ∞) set of energies, in which case you'd be hosed anyways. --Laura Scudder 23:46, 4 Apr 2005 (UTC)

Actually you brought forward something that I didn't consider before! We should explain this subtlety about the infinite/semi-infinite set of energies available to the system. The | > state is only needed in the case where the energies are semi-infinite, such as the quantum harmonic oscillator. In the quantum harmonic oscillator, it's necessary to define |0> as the "ground" state of the system, which arguably already has 1 quanta of energy in it, and | > the completely "null" state where there's absolutely no energy whatsoever in the oscillator. It's necessary to explain why the annihilation operation a|0> = 0. It's because it really is a short form for a|0> = 0| > = 0, since 0 is the eigenvalue for the |0> state. However, admittingly, this is somewhat of a subtle point that isn't often mentioned, although in Wikipedia, there is a reference to the "zero ket" in quantum harmonic oscillator about halfway down the page. I'll attempt to add this to the page – please feel free to modify it if necessary :) HappyCamper 14:43, 5 Apr 2005 (UTC)