Momentum Dispersion

T.T. TAYLOR

Ravo Tokiniaina Ranaivoson

This paper is a continuation of our previous works about coordinate, momentum, dispersion operators and phase space representation of quantum mechanics. It concerns a study on the properties of wavefunctions in the phase space representation and the momentum dispersion operator, its representations and eigenvalue equation. After the recall of some results from our previous papers, we give most of the main properties of the phase space wavefunctions and consider some examples of them. Then we establish the eigenvalue equation for the differential operator corresponding to the momentum dispersion operator in the phase space representation. It is shown in particular that any phase space wavefunction is solution of this equation.

Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Hanitriarivo Rakotoson

This paper is a continuation of our previous works concerning coordinate, momentum, dispersion operators and phase space representation of quantum mechanics. It deals with the properties of momentum dispersion operator, its representations, eigenvalue equation and its relations with the wavefunctions in the phase space representation. After recalling some results from our previous works, we perform a study concerning the phase space wavefunctions and consider some example of them. Then we establish the eigenvalue equation for the differential operator corresponding to the momentum dispersion operator in the phase space representation. It is shown in particular that any wavefunction in phase space representation is solution of this equation.

James M. Feagin

M Mohammadi, M. H. Naderi, M. Soltanolkotabi

We present a theoretical scheme based on su(2) algebra to investigate the influence of homogeneous gravitational field on the quantum nondemolition measurement of atomic momentum in dispersive Jaynes-Cummings model. In the dispersive Jaynes-Cummings model, when detuning is large and the atomic motion is in a propagating light wave, we consider a two-level atom with quantized cavity-field in the presence of a homogeneous gravitational field. We derive an effective Hamiltonian describing the dispersive atom-field interaction in the presence of gravitational field. We can see gravitational influence both on the momentum filter and momentum distribution. Moreover, gravitational field decreases both tooth spacing of momentum and the width of teeth of momentum.

Leon W. Cohen