Solution of the Schr?dinger Equation for a Linear Potential using the Extended Baker-Campbell-Hausdorff Formula

Authors

Francisco Soto-Eguibar, Instituto Nacional de Astrof´ısica, ´Optica y Electr´onica, INAOE. Luis Enrique Erro 1, Santa Mar´ıa Tonantzintla, San Andr´es Cholula, Puebla, 72840, M´exicoFollow
Héctor M. Moya-Cessa, Instituto Nacional de Astrof´ısica, ´Optica y Electr´onica, INAOE. Luis Enrique Erro 1, Santa Mar´ıa Tonantzintla, San Andr´es Cholula, Puebla, 72840, M´exicoFollow

Author Country (or Countries)

M´exico

Abstract

The time-dependent Schr¨odinger equation is solved for a linear potential using operational methods; in particular, an extension of the Baker-Campbell-Hausdorff formula is exposed and used. Several initial conditions are considered. A closed formfor the Wigner function is presented. The results can be extended to the propagation of an electromagnetic field in the paraxial approximation.

Digital Object Identifier (DOI)

http://dx.doi.org/10.12785/amis/090123

Recommended Citation

Soto-Eguibar, Francisco and M. Moya-Cessa, Héctor (2015) "Solution of the Schr?dinger Equation for a Linear Potential using the Extended Baker-Campbell-Hausdorff Formula," Applied Mathematics & Information Sciences: Vol. 09: Iss. 1, Article 30.
DOI: http://dx.doi.org/10.12785/amis/090123
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss1/30