Far East Journal of Applied Mathematics

The Far East Journal of Applied Mathematics publishes original research papers and survey articles in applied mathematics, covering topics such as nonlinear dynamics, approximation theory, and mathematical modeling. It encourages papers focusing on algorithm development.

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TIME-DEPENDENT SCHRÖDINGER EQUATION: I. LONGITUDE GAUGE

Authors

  • Alejandro Palma

Keywords:

Lie algebra, Klein-Gordon equation.

DOI:

https://doi.org/10.17654/0972096022008

Abstract

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].

Received: February 2, 2022
Accepted: March 14, 2022

References

F. Capasso, K. Mohammed and A. Y. Cho, Perspectives in Condensed Matter Physics (A Critical Reprint Series), Vol. 1, Springer, 1988.

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.

I. Urdaneta, A. Keller, O. Atabek and V. Mujica, Laser-induced nonlinear response in photoassisted resonant electronic transport, J. Chem. Phys. 127 (2007), 154110.

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.

J. Wei and E. Norman, Lie algebraic solution of linear differential equations, J. Math. Phys. 4 (1963), 575-581.

D. M. Volkov, Über eine Klasse von Lösungen der Diracschen Gleichung, Z. Physik 94 (1935), 250-260.

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Published

2022-03-29

Issue

Vol. 113 (2022)

Section

Articles

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How to Cite

TIME-DEPENDENT SCHRÖDINGER EQUATION: I. LONGITUDE GAUGE. (2022). Far East Journal of Applied Mathematics, 113, 29-35. https://doi.org/10.17654/0972096022008

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