Dunkl-Schrödinger Equation with Time-Dependent Harmonic Oscillator Potential

Abstract

This paper presents an investigation into one- and three-dimensional harmonic oscillators with time-dependent mass and frequency, within the framework of the Dunkl formalism, which is constituted by replacing the ordinary derivative with the Dunkl derivative. To ascertain a general form of the wave functions the Lewis-Riesenfeld method was employed. Subsequently, an exponentially changing mass function in time was considered and the parity-dependent quantum phase, energy eigenvalues, and the corresponding wave functions were derived in one dimension. The findings revealed that the mirror symmetries affect the wave functions, thus the associated probabilities. Finally, the investigation was extended to the three-dimensional case, where it was demonstrated that, as with the solution of the radial equation, the solutions of the angular equation could be classified according to their mirror symmetries.