Method of Coherent States

Abdulmuhsen H. Ali

A derivation of the statistical nature of quantum probabilities is presented by considering a system of bosonic particles in a coherent state. A comparison between the current approach and a former derivation is also discussed. The current approach, which is an evaluation of the field operator matrix in the coherent Glauber state, proved to be a concise method which can be applied to relativistic particles as well. An extension of the coherent state method to the fermionic type of particles is also presented and thus the generality of the coherent state method is established.

R. Roknizadeh, Mohammad Kazem Tavassoly

Considering some important classes of generalized coherent states known in literature, we demonstrated that all of them can be created via conventional fashion, i.e. the "lowering operator eigen-state" and the "displacement operator" techniques using the {\it "nonlinear coherent states"} approach. As a result we obtained a {\it "unified method"} to construct a large class of coherent states which already have been introduced by different prescriptions.

Peter W. Milonni, Michael Martin Nieto

Sh. M. Nagiyev, E. I. Jafarov

Abstract We present details of the method for constructing the coherent states of the quantum harmonic oscillator model that exhibits the semiconfinement effect due to a specific change of its mass by position. Its energy spectrum completely overlaps with the Hermite oscillator energy spectrum, whereas the wavefunctions of the stationary states are expressed via the generalized Laguerre polynomials. Two different methods have been applied to compute the coherent states. They are generalized and Barut-Girardello coherent states methods. In both cases, the exact expressions have been obtained. We also analyzed some limit cases, under which the constructed coherent states completely recover the coherent states of the Hermite oscillator.