Coherent states and related quantizations for unbounded motions

M. C. Ashworth

V G Bagrov, Jean‐Pierre Gazeau, D M Gitman +1 more

We discuss the construction of coherent states (CS) for systems with continuous spectra. First, we propose to adopt the Malkin–Manko approach, developed for systems with discrete spectra, to the case under consideration. Following this approach, we consider two examples, a free particle and a particle in a linear potential. Second, we generalize the approach of action-angle CS to systems with continuous spectra. In the first approach we start with a well-defined quantum formulation (canonical quantization) of a physical system and the construction of CS follows from such a quantization. In the second approach, the quantization procedure is inherent to the CS construction itself.

Isiaka Aremua, Komi Sodoga, P.K. Tchakpélé

This work addresses the general procedure of quantization also known as the Berezin-Klauder-Toeplitz quantization, or as coherent state (CS) (anti-Wick) quantization. The method is first illustrated by the motion of a particle on the circle. Then, we take as second example, a set of generalized photon-added coherent states related to associated hypergeometric functions. The nonclassical behaviour of this set of coherent states is also investigated.

John R. Klauder

S. Twareque Ali

Ingrid C. Daubechies

We use the properties of an integral transform relating a classical function f with the matrix elements between coherent states of its quantal counterpart Q f, to derive continuity properties of the Weyl transform from classes of distributions to classes of quadratic forms. We also give examples of pathological behavior of the Weyl transform with respect to other topologies (e.g., bounded functions leading to unbounded operators).