Path integral formulation for Dunkl-Dirac oscillator in (1+1)-dimensional space-time coordinates
H. Benzair, T. Boudjedaa, M. Merad
Abstract
Abstract In this paper, we extend the path integral formalism for the Dirac oscillator in (1+1) dimension by replacing the spatial derivative with the Dunkl derivative. Utilizing representations in position space-time coordinates, we precisely calculate the propagator, expressed in terms of generalized Hermite polynomials. The energy eigenvalues of the electron, along with their corresponding wave functions, are determined. In special cases, we can precisely evaluate the non-relativistic energy eigenvalues and wave functions, even in the absence of Dunkl parameters.
Topics & Concepts
Space (punctuation)Dirac (video compression format)Path integral formulationPath (computing)Dirac equationMathematical analysisPhysicsMathematical physicsMathematicsQuantum mechanicsComputer scienceNeutrinoProgramming languageOperating systemQuantumQuantum Mechanics and Non-Hermitian PhysicsAlgebraic and Geometric AnalysisNoncommutative and Quantum Gravity Theories