Studies in Quantum Oscillators and q-Deformed Quantum Mechanics

Alexander A. Andrianov, F. Cannata, J.-P. Dedonder +1 more

Jian-zu Zhang

Sepideh Sargolzaeipor, HASSAN HASSANABADI, Won Sang Chung

In this article, we introduce a two-dimensional Dirac oscillator in the presence of an external magnetic field in terms of q-deformed creation and annihilation operators in the framework of relativistic quantum mechanics with minimal length. We discuss the eigenvalues of q-deformed Dirac oscillator in two dimensions and report the statistical quantities of the system for a small real q.

Won Sang Chung, Abdullah Algin

Abstract In this paper, we consider a system of the q-deformed bosonic Tamm-Dancoff oscillators, whose spectrum has some exponential cutoff factors at high energies. We first investigate the q-calculus in the Tamm-Dancoff (TD) boson algebra, and within this framework, the q-derivative, q-integral and q-exponential function are introduced. Using these properties, we construct a new formalism for the q-deformed quantum mechanics, which accordingly involve the q-adjoint operator and the q-Hermitian operator properties. We then derive the q-deformed Heisenberg relation, and develop the q-Hermitian momentum operator. The q-deformed Schrödinger equation is introduced, and as applications, we study the momentum eigenfunction and one-dimensional box problem. Another application of the TD type deformation onto lattice oscillations is also discussed through a model of the q-deformed Debye solid. Finally, other potential applications of the TD-oscillators gas model are concisely pointed out.

J. Batouli, M. El Baz

Bruno G. da Costa, Ernesto P. Borges