Abstract

It has been known for some time that the infinite-dimensional Hilbert space H used for modelling quantum mechanically a mode of the electromagnetic field has not been entirely adequate.¹ Of particular concern in recent times is the problem of incorporating a quantum-mechanical description of phase.^2-4 A few years ago Pegg and Barnett introduced the Ψ-space formalism,⁵ based on finite-dimensional spaces Ψ, which allows sensible phase properties of states of the field to be calculated. This formalism requires a particular limiting procedure in which the infinite dimensional limits are taken of expectation values only after all other calculations have been made on the finite dimensional spaces Ψ.

© 1994 IEEE