q-Deformed Oscillators in Nuclear and Molecular Physics

Dennis Bonatsos A

JoséLuis Gruver

Ramandeep S. Johal, Raj K. Gupta

q-deformed harmonic oscillator is established for any arbitrary complex q-deformation parameter (with real and imaginary q as its special cases) and the formalism so developed is used to construct the quantum group SUq(2). The eigenvalues of the Casimir of SUq(2) are now real, even for complex q-deformation (q=ea+ib). This happens for (a,b)≪1. Thus, the use of real part of energies in the earlier works of Gupta and collaborators7–14 is mathematically rigorous, since only small values of (a, b) are involved in all the nuclear and molecular physics problems studied7–14,18–20 so far.

G Vinod

Joseph L. Birman

J. Cseh

Investigates the question of whether or not the vibrational spectrum of a two-dimensional interacting boson model can be transformed into the rotational one via quantum deformation of the group structure. It turns out that although the spectrum of the q-deformed model shows one or another of the rotational-like features at different values of the deformation parameter, nevertheless, all the requirements of the rotational behavior cannot be obtained simultaneously. This result indicates that the quantum algebraic treatment cannot give an analytical solution to the eigenvalue problem of the interacting boson models of nuclear and molecular physics in the whole range of the physically relevant breaking of dynamical symmetries.