Quantum Oscillators: General Considerations

Olivier Henri‐Rousseau, Paul Blaise

Ha Huy Bang

The generalized deformed uncertainty principle is derived and the connections of some deformed quantities with the usual ones are studied. Furthermore, taking into consideration the expressions of the quantum fields in terms of the generalized deformed oscillators we can find some special deformations, in which the corresponding deformed quantum fields are local and deformed oscillators are linear.

M. G. A. Crawford

Many generalizations of the harmonic oscillator coherent states are known in the literature. One such generalization by Nieto has been applied to a particular system known as the `harmonic oscillator with centripetal barrier'. In this paper, it is shown that Nieto's generalization in this system may be described in terms of a recent generalization due to Klauder. This is of considerable interest since the approaches to generalizing coherent states differ significantly.

A. M. Perelomov

Carlo Heissenberg, Augusto Sagnotti

J. Beckers, N. Debergh

Generalized coherent states for the one-dimensional harmonic oscillator with maximal symmetry, i.e., admitting the semidirect sum so(2,1) ⧠ h(2) as the largest invariance Lie algebra pointed out by Niederer are constructed. The normalization of such states as well as their completeness property are determined and discussed. They are also analyzed in the subcontexts of the so(2,1) algebra and of the Heisenberg h(2) algebra. General considerations on Heisenberg relations, on minimal dispersions, and on quantum mechanical entropies are presented in connection with the uncertainty principle.