Energy of interacting particle and time evolution of p(x)

[jshrager]

In classical QM, using a photon to measure the location or momentum of an electron collapses the electron's wave function at the point of measurement, which then, over time, spreads out again (what I'll call "diffuses"). Fine. The question is: Does the energy of the measuring photon change the time course of the diffusion process, and if so, in which direction? I.e., does a higher energy photon lead to a faster or slower diffusion, or no change at all? Does the answer differ if the energy of the measuring photon is increased by virtue of wavelength (i.e., more blue) v. being multiple coherent photons at the same wavelength (e.g., from a laser)?

 

[mfb]

It depends on the setup. A scattered photon (i. e. a "measurement") changes the momentum of the particle, and a photon of higher energy (with the same scattering angle) will transfer more momentum on the particle. The uncertainty, however, can be different and depends on the setup.