New operator realization of angular momentum for description of electron's motion in uniform magnetic field

Abstract

By introducing appropriate electron's coordinate eigenstate and momentum eigenstate we propose new realization of angular momentum operators for describing electron's motion in uniform magnetic field. The coordinate eigenstates make up a representation and embody quantum entanglement between magnetic field and electron. The eigenstate of angular momentum's lowering-ascending operator L_± are derived, the way we tackle this problem is to make an analogue between the transform $e^{2f{L}_z}{L}_{\pm }{e}^{-2f{L}_z}$ to the squeezing mechanism. All these discussions reveal that the quantum theory for charged particles' motion in magnetic field needs to be developed.