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Exact Solution of the Relativistic Dunkl Oscillator in $(2+1)$ Dimensions. (arXiv:1812.05207v1 [math-ph])
来源于:arXiv
In this paper we study the $(2+1)$-dimensional Dirac-Dunkl oscillator coupled
to an external magnetic field. Our Hamiltonian is obtained from the standard
Dirac oscillator coupled to an external magnetic field by changing the partial
derivatives by the Dunkl derivatives. We solve the Dunkl-Klein-Gordon-type
equations in polar coordinates in a closed form. The angular part
eigenfunctions are given in terms of the Jacobi-Dunkl polynomials and the
radial functions in terms of the Laguerre functions. Also, we compute the
energy spectrum of this problem and show that, in the non-relativistic limit,
it properly reduces to the Hamiltonian of the two dimensional harmonic
oscillator. 查看全文>>