Generalized coherent states for discrete and continuous dynamics and their applications

A. M. Perelomov

S A Pol'shin

We construct the systems of generalized coherent states for the discrete and continuous spectra of the hydrogen atom. These systems are expressed in elementary functions and are invariant under the SO (3, 2) (discrete spectrum) and SO (4, 1) (continuous spectrum) subgroups of the dynamical symmetry group SO (4, 2) of the hydrogen atom. Both systems of coherent states are particular cases of the kernel of integral operator which intertwines irreducible representations of the SO (4, 2) group.

A. M. Perelomov

John R. Klauder

Coherent states for general systems with discrete spectrum, such as the bound states of the hydrogen atom, are discussed. The states in question satisfy: (1) continuity of labeling, (2) resolution of unity, (3) temporal stability, and (4) an action identity. This set of reasonable physical requirements uniquely specify coherent states for the (bound state portion of the) hydrogen atom.

T Lisowski

The classical discrete dynamics generated by the squeezing Hamiltonian can be extracted from the expression for the path integral over the SU(1,1) coherent states in the continuous limit. In this letter the general formulae for the expectation values of the Hamiltonians of this type in these states are presented.

Snehasis Bera, Sourav Das, Abhijit Banerjee

In this work, an extensive class of coherent states is introduced by taking the Fox Wright function as the normalization function. It is demonstrated that these states satisfy the key requirements of continuity, normalizability and resolution of unity. Furthermore, coherent states associated with the continuous spectrum are obtained through a discrete to continuous limiting procedure. Moreover, FW generalized multi parameter nu function is introduced and shown to act as the normalization function for the Fox Wright coherent states in the continuous spectrum. Later the Fox Wright function with bicomplex arguments has been introduced and its existence has been investigated. Bicomplex Fox Wright coherent states are also developed for the discrete spectrum based on this new function and their properties are analyzed. Subsequently, the results regarding Fox Wright coherent states are generalized to the bicomplex setting. In addition, a bicomplex FW generalized multi-parameter nu function is defined to demonstrate that it provides the normalization for these states in the continuous spectrum.