Eur. Phys. J. Plus (2019) 134: 606
https://doi.org/10.1140/epjp/i2019-12962-9

Regular Article

Sp(4, R) algebraic approach of the most general Hamiltonian of a two-level system in two-dimensional geometry

¹ Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, Delegación Gustavo A. Madero, C.P. 07738, Ciudad de México, Mexico
² Escuela Superior de Cómputo, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz esq. Av. Miguel Othón de Mendizábal, Col. Lindavista, Delegación Gustavo A. Madero, C.P. 07738, Ciudad de México, Mexico

^* e-mail: dojedag@ipn.mx

Received: 22 February 2019
Accepted: 27 August 2019
Published online: 5 December 2019

Abstract

In this paper we study the interaction part of the most general Hamiltonian of a two-level system in two-dimensional geometry. We decouple the equations for each spinor component and diagonalize them using the similarity transformations of the Sp(4, R) group. Then, we obtain the energy spectrum of this general Hamiltonian and show that its eigenfunctions are the Sp(4, R) group coherent states. As particular cases of this Hamiltonian, we reproduce the solution of earlier problems as the Dirac oscillator and the Jaynes-Cummings model with one and two modes of oscillation.