Exact solutions of the Schrödinger Equation with Dunkl Derivative for the Free-Particle Spherical Waves, the Pseudo-Harmonic Oscillator and the Mie-type Potential

Abstract

We solve exactly the Schrödinger equation for the free-particle, the pseudo-harmonic oscillator and the Mie-type potential in three dimensions with the Dunkl derivative. The equations for the radial and angular parts are obtained by using spherical coordinates and separation of variables. The wave functions and the energy spectrum for these potentials are derived in an analytical way and it is shown that our results are adequately reduced to those previously reported when we remove the Dunkl derivative parameters.

10 pages

References in corpus (1)

• $SU(1,1)$ solution for the Dunkl oscillator in two dimensions and its coherent states

Cited by in corpus (11)

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• Ideal Bose Gas and Blackbody Radiation in the Dunkl Formalism
• The condensation of ideal Bose gas in a gravitational field in the framework of Dunkl-statistic
• Dunkl-Pauli Equation in the Presence of a Magnetic Field
• Dunkl-Schrödinger equation with time-dependent harmonic oscillator potential
• Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential
• A Path Integral Treatment of Time-dependent Dunkl Quantum Mechanics
• Time-dependent Dunkl-Pauli Oscillator