They seem the same to me. You regard both light waves and the electron clouds around atoms as collections of harmonic oscillators and quantize them. But that seems to me to be a departure from the original conception of the wave function a la Shrodinger and Born. Born claimed the De Broglie wave was NOT a classical wave in space but a mathematical description of the state of the body “associated” with the wave, whereas a light wave is definitely a wave in space. He was hard pressed to explain why two of these “mathematical descriptions” could interfere with each other and give interference patterns, but he always maintained an electron, or any other massive body, was a particle and not a wave or “part” of a wave.
Except the creation and annihilation operators in one obey canonical commutation relations, and in the other they obey canonical anticommutation relations.
But QFT doesn’t say these are “the wavefunction” any more. They’re just basic field excitations. We do get the wavefunction back later, as I’ve already described.
I guess thats the part I don’t understand. I don’t know how you get a wavefunction back. and, I have also heard it said that the photon has no wavefunction because (I think) it can’t be localized in space without destroying it.
Actually, that’s not his motivation. Even if there are no other monopoles, you could still have an extreme Reissner-Nordstrom black hole with a single fundamental magnetic charge. Such a beast could presumably be produced by vacuum polarization by a sufficiently-strong magnetic field, and if there are no lighter monopoles, it would even be stable. The catch, of course, is that sufficiently-strong magnetic fields would be practically impossible to produce, especially in the post-inflationary Universe, so we shouldn’t be surprised if there aren’t any monopole holes in observable space.
It’s fairly easy to build a monopole detector, and some folks at Stanford did just that. Any observations were expected to be rather fleeting, since all the basic detector design does is tell you whether a monopole passed through a particular coil of wire, and what it’s charge was. One of their detectors did, in fact, register that a monopole passed through it, with the same charge as is predicted theoretically, but the event has never repeated. To this day, nobody’s quite sure what happened there, whether it was a genuine but rare event that we just happened to luck out and see, a glitch in the equipment which was coincidentally just the right size, or a hoax by somewone with access to the experiment.
Set up the S-matrix, which gives the transition amplitudes from instates to outstates. Then put in your initial conditions as the instate and you get the transition amplitudes for all possible outstates. That’s the wavefunction.
45 posts in and still no grand unified theory? Come on, people, the SDMB has a reputation to uphold.
Just you wait; when it gets posted, it won’t be in General Questions. It’ll pop up in MPSIMS as the Monday Morning Post.
I remember that!!!
Didn’t the guy write “WOW!” on the sheet or sumthin’?
That was looking for radio signals from extraterrestrial intelligences