Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential

• URL: http://arxiv.org/abs/2408.02021v1
• Date: Sun, 4 Aug 2024 13:11:52 GMT
• Title: Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential
• Authors: B. Khantoul, B. Hamil, A. Benchikha, B. C. Lütfüoğlu,
• Abstract summary: The Schr"odinger equation is a fundamental equation in quantum mechanics. Over the past decade, theoretical studies have focused on adapting the Dunkl derivative to quantum mechanical problems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Schr\"odinger equation is a fundamental equation in quantum mechanics, providing a means of understanding the behavior of quantum systems under a range of potential energies. In particular, over the past decade, theoretical studies have focused on adapting the Dunkl derivative to quantum mechanical problems. This approach merely seeks to generalize traditional quantum mechanical techniques through the utilization of differential-difference operators associated with finite reflection groups, thereby providing solutions that are dependent on parity. In this manuscript, we investigate the analytical solution of the time-dependent Schr\"odinger equation for a harmonic oscillator with time-dependent mass and frequency, coupled with angular-dependent potential energy by utilizing the Dunkl derivatives. To obtain the solution, we employ the Lewis-Riesenfeld invariant methodology. Our approach broadens the scope of quantum mechanical analyses, offering exact solutions and new insights into dynamic quantum systems under varying conditions.

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