A Path Integral Treatment of Time-dependent Dunkl Quantum Mechanics
arXiv:2410.20531 · doi:10.1142/S0219887825501130
Abstract
This paper presents an analytical treatment of the path integral formalism for time-dependent quantum systems within the framework of Wigner-Dunkl mechanics, emphasizing systems with varying masses and time-dependent potentials. By employing generalized canonical transformations, we reformulated the path integral to develop an explicit expression for the propagator. This formalism is applied to specific cases, including a Dunkl-harmonic oscillator with time-dependent mass and frequency. Solutions for the Dunkl-Caldirola-Kanai oscillator and a model with a strongly pulsating mass are derived, providing exact propagator expressions and corresponding wave functions. These findings extend the utility of Dunkl operators in quantum mechanics, offering new insights into the dynamics of time-dependent quantum systems.
14 pages
References in corpus (32)
- Exchange Operator Formalism for Integrable Systems of Particles
- Deformed Heisenberg algebra, fractional spin fields and supersymmetry without fermions
- Self-isospectrality, special supersymmetry, and their effect on the band structure
- Anyon wave equations and the noncommutative plane
- Hidden supersymmetry in quantum bosonic systems
- The Dunkl oscillator in the plane I : superintegrability, separated wavefunctions and overlap coefficients
- Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system
- The Dunkl oscillator in three dimensions
- Exact Solutions of the 2D Dunkl--Klein--Gordon Equation: The Coulomb Potential and the Klein--Gordon Oscillator
- Deformed Heisenberg algebra and fractional spin field in 2+1 dimensions
- solution for the Dunkl oscillator in two dimensions and its coherent states
- Dunkl-Klein-Gordon equation in three-dimensions: The Klein-Gordon oscillator and Coulomb Potential
- Hidden nonlinear supersymmetry of finite-gap Lame equation
- Thermal Properties of Relativistic Dunkl Oscillators
- Dunkl-Graphene in constant magnetic field
- Exact solutions of the Schrödinger Equation with Dunkl Derivative for the Free-Particle Spherical Waves, the Pseudo-Harmonic Oscillator and the Mie-type Potential
- Hidden nonlinear su(2|2) superunitary symmetry of N=2 superextended 1D Dirac delta potential problem
- Nonlinear supersymmetry in the quantum Calogero model
- On the Path Integral Formulation of Wigner-Dunkl Quantum Mechanics
- Relativistic Solutions of Generalized-Dunkl Harmonic and Anharmonic Oscillators
- Ideal Bose Gas and Blackbody Radiation in the Dunkl Formalism
- Conformal bridge between asymptotic freedom and confinement
- Rationally-extended Dunkl oscillator on the line
- Dunkl-Pauli Equation in the Presence of a Magnetic Field
- Quadratic Time-dependent Quantum Harmonic Oscillator
- Dunkl-Schrödinger equation with time-dependent harmonic oscillator potential
- On the two-dimensional time-dependent anisotropic harmonic oscillator in a magnetic field
- One-dimensional Dunkl Quantum Mechanics: A Path Integral Approach
- Exact solutions of a damped harmonic oscillator in a time dependent noncommutative space
- Exact solution of damped harmonic oscillator with a magnetic field in a time dependent noncommutative space
- Continuous-time quantum harmonic oscillator state engineering
- Weak-strong duality of the non-commutative Landau problem induced by a two-vortex permutation, and conformal bridge transformation