Green’s functions of relativistic oscillators with generalized Dunkl derivative: the (1+1)-dimensional case

2024/12/13 by Djamel E M Raber, H. Benzair, Hadjira Benzair +4 · 2 citations
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Neutrino Physics Research

paper · doi:10.1088/1402-4896/ad9efa

Abstract

Abstract The Green’s functions for relativistic oscillators with spin-0 and spin-1/2, within the framework of a new generalization of the Dunkl derivative with three parameters, are calculated using the path integral approach. For simplicity, this derivative is reformulated to depend on only two parameters. As a result, the energy eigenvalues and their corresponding wave functions are determined in both cases as functions of the three deformed parameters. In the limiting cases of the deformed parameters, the standard Dunkl derivative system is recovered, even in the absence of the Dunkl parameters.

Citations

• Differential-difference operators associated to reflection groups

Cited by

• A generalization of the parametric amplifier with Dunkl derivative: spectral and statistical properties
• Exact Solutions of the Schrödinger-Dunkl Equation for a Free Particle in a Finite and Infinite Cylindrical Well

Related

• Relativistic solutions of generalized-Dunkl harmonic and anharmonic oscillators
• Green's Function of the Relativistic Coulomb System via Duru-Kleinert Method
• Algebraic approach for the one-dimensional Dirac–Dunkl oscillator
• Effect of the two-parameter generalized Dunkl derivative on the two-dimensional Schrödinger equation
• DKP equation in Wigner–Dunkl quantum mechanics framework