Phase Operator Theory for an Electron Moving in a Uniform Magnetic Field

We show that the newly found complete and orthonormal representation <λ|, which is constructed in terms of guiding centers and canonical momenta of an electron moving in a uniform magnetic field, also helps us to establish a systematic phase operator theory. The unitary phase operator, interpreted as a quantity canonically conjugated to the electron angular momentum, manifestly exhibits in the <λ| representation its phase behavior. As a byproduct, the phase distribution function, in the correct sense of probability in quantum mechanics, can also be defined by the <λ| representation.