CharlesEGrant
27-June-2005, 12:02 AM
A zillion years ago I took an introductory course in quantum electrodynamics. Yesterday I was about to put my nickel in on a thread in the ATM forum that touched on whether photons had spatial extent, when I suddenly realized I had no idea what I was talking about.
It occurred to me that, although I'd seen a thousand casual reference to the wave function of a photon, I'd never actually seen a photon wave function derived ala Schrodinger or Dirac. I looked at a couple of old texts I had laying around, Saukarai's Advanced Quantum Mechanics, and Heitler's Quantum Theory of Radiation, and sure enough the textbook models for the photon in QED don't talk about photon wave functions, but about creation and destruction operators for quantized excitations of the EM field. Furthermore, these quanta are eigenstates of momentum and so are completely de-localized. (Heilter even comments that there is no simple interpretation for the position of a photon.) I think for most of us lay people, localization is the essential attribute of particle-ness, so suddenly photons aren't sounding very particle-like to me.
Is there a disconnect between casual descriptions of a photon as a particle and the formal model of a photon as a quantized excitation of a field? Can anyone point me to a derivation of a wave function for a photon? I'm a bit worried that the typical popular and semi-popular explanations of the two-slit experiment casually assume the existence of a de Broglie wave function for both photons and electrons. I've certainly repeated these explanations often enough, and I'd hate to think that I'd been misleading people. Thanks in advance for your pointers and comments.
It occurred to me that, although I'd seen a thousand casual reference to the wave function of a photon, I'd never actually seen a photon wave function derived ala Schrodinger or Dirac. I looked at a couple of old texts I had laying around, Saukarai's Advanced Quantum Mechanics, and Heitler's Quantum Theory of Radiation, and sure enough the textbook models for the photon in QED don't talk about photon wave functions, but about creation and destruction operators for quantized excitations of the EM field. Furthermore, these quanta are eigenstates of momentum and so are completely de-localized. (Heilter even comments that there is no simple interpretation for the position of a photon.) I think for most of us lay people, localization is the essential attribute of particle-ness, so suddenly photons aren't sounding very particle-like to me.
Is there a disconnect between casual descriptions of a photon as a particle and the formal model of a photon as a quantized excitation of a field? Can anyone point me to a derivation of a wave function for a photon? I'm a bit worried that the typical popular and semi-popular explanations of the two-slit experiment casually assume the existence of a de Broglie wave function for both photons and electrons. I've certainly repeated these explanations often enough, and I'd hate to think that I'd been misleading people. Thanks in advance for your pointers and comments.