TY - JOUR
T1 - Energy Power Series Analysis of the Bound States of the One-dimensional Dirac Equation
AU - Barrera-Figueroa, V.
N1 - Publisher Copyright:
© Published under licence by IOP Publishing Ltd.
PY - 2023
Y1 - 2023
N2 - In this work we consider the one-dimensional Dirac equation including an electrostatic potential with compact support, and focus on the regime of bound states. We obtain exact expressions for both the characteristic function and the eigenfunctions in L 2 (R , C 2), given in the form of power series of the energy parameter. This approach is meant for arbitrary bounded potentials, so that a square potential is a special case of the theory here presented. We derive an efficient numerical method for the calculation of approximate eigen-energies of the bound states. Finally, we investigate the physical sense of the eigen-energies that are forbidden in the non-relativistic regime in terms of the Klein tunneling.
AB - In this work we consider the one-dimensional Dirac equation including an electrostatic potential with compact support, and focus on the regime of bound states. We obtain exact expressions for both the characteristic function and the eigenfunctions in L 2 (R , C 2), given in the form of power series of the energy parameter. This approach is meant for arbitrary bounded potentials, so that a square potential is a special case of the theory here presented. We derive an efficient numerical method for the calculation of approximate eigen-energies of the bound states. Finally, we investigate the physical sense of the eigen-energies that are forbidden in the non-relativistic regime in terms of the Klein tunneling.
UR - http://www.scopus.com/inward/record.url?scp=85150031641&partnerID=8YFLogxK
U2 - 10.1088/1742-6596/2448/1/012010
DO - 10.1088/1742-6596/2448/1/012010
M3 - Artículo de la conferencia
AN - SCOPUS:85150031641
SN - 1742-6588
VL - 2448
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
IS - 1
M1 - 012010
T2 - 9th International Conference on Quantum Phenomena, Quantum Control and Quantum Optics, Quantum Fest 2021
Y2 - 25 October 2021 through 29 October 2021
ER -