TIME-DEPENDENT SCHRÖDINGER EQUATION: I. LONGITUDE GAUGE
Many systems studied in physics concern with barrier potentials immersed in a statical electric field, the tunnelling resonance being the entire field of research [1]. It is common to apply an oscillating field to these systems, and the Gordon-Volkov wave functions are solutions to such systems, which are classically found using ansatz. In this paper, we find the exact algebraical solution under the length gauge using the method developed by Wei and Norman [5].
Lie algebra, Klein-Gordon equation.
Received: February 2, 2022; Accepted: March 14, 2022; Published: March 29, 2022
How to cite this article: Alejandro Palma, Time-dependent Schrödinger equation: I. Longitude gauge, Far East Journal of Applied Mathematics 113 (2022), 29-35. http://dx.doi.org/10.17654/0972096022008
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] F. Capasso, K. Mohammed and A. Y. Cho, Perspectives in Condensed Matter Physics (A Critical Reprint Series), Vol. 1, Springer, 1988.[2] R. Lefebvre, Resonant tunneling in the presence of two electric fields: one static and the other oscillating, International Journal of Quantum Chemistry 80 (2000), 110-116.[3] I. Urdaneta, A. Keller, O. Atabek and V. Mujica, Laser-induced nonlinear response in photoassisted resonant electronic transport, J. Chem. Phys. 127 (2007), 154110.[4] R. A. Sacks and A. Szöke, Electron scattering assisted by an intense electromagnetic field: exact solution of a simplified model, Phys. Rev. A Gen. Phys. 40(10) (1989), 5614-5632.[5] J. Wei and E. Norman, Lie algebraic solution of linear differential equations, J. Math. Phys. 4 (1963), 575-581.[6] D. M. Volkov, Über eine Klasse von Lösungen der Diracschen Gleichung, Z. Physik 94 (1935), 250-260.