TY - JOUR
T1 - Algebraic approach for the one-dimensional Dirac-Dunkl oscillator
AU - Ojeda-Guillén, D.
AU - Mota, R. D.
AU - Salazar-Ramírez, M.
AU - Granados, V. D.
N1 - Publisher Copyright:
© 2020 World Scientific Publishing Company.
PY - 2020/10/10
Y1 - 2020/10/10
N2 - We extend the (1 + 1)-dimensional Dirac-Moshinsky oscillator by changing the standard derivative by the Dunkl derivative. We demonstrate in a general way that for the Dirac-Dunkl oscillator be parity invariant, one of the spinor component must be even, and the other spinor component must be odd, and vice versa. We decouple the differential equations for each of the spinor component and introduce an appropriate su(1, 1) algebraic realization for the cases when one of these functions is even and the other function is odd. The eigenfunctions and the energy spectrum are obtained by using the su(1, 1) irreducible representation theory. Finally, by setting the Dunkl parameter to vanish, we show that our results reduce to those of the standard Dirac-Moshinsky oscillator.
AB - We extend the (1 + 1)-dimensional Dirac-Moshinsky oscillator by changing the standard derivative by the Dunkl derivative. We demonstrate in a general way that for the Dirac-Dunkl oscillator be parity invariant, one of the spinor component must be even, and the other spinor component must be odd, and vice versa. We decouple the differential equations for each of the spinor component and introduce an appropriate su(1, 1) algebraic realization for the cases when one of these functions is even and the other function is odd. The eigenfunctions and the energy spectrum are obtained by using the su(1, 1) irreducible representation theory. Finally, by setting the Dunkl parameter to vanish, we show that our results reduce to those of the standard Dirac-Moshinsky oscillator.
KW - Dirac equation
KW - Dirac-Moshinsky oscillator
KW - Dunkl derivative
KW - Lie algebras
UR - http://www.scopus.com/inward/record.url?scp=85093839257&partnerID=8YFLogxK
U2 - 10.1142/S0217732320502557
DO - 10.1142/S0217732320502557
M3 - Artículo
AN - SCOPUS:85093839257
SN - 0217-7323
VL - 35
JO - Modern Physics Letters A
JF - Modern Physics Letters A
IS - 31
M1 - 2050255
ER -