Gamow vectors and Supersymmetric Quantum Mechanics

Oscar Rosas–Ortiz

Departamento de Física, Cinvestav, A.P. 14–740, México 07000, D.F. México

Recibido el 18 de julio de 2005
Aceptado el 14 de marzo de 2005

Abstract

Gamow solutions are used to transform self–adjoint energy operators by means of factorization (supersymmetric) techniques. The transformed non–hermitian operators admit a discrete real spectrum which is occasionally extended by a single complex eigenvalue associated to normalized eigensolutions. These new Hamiltonians are not pseudo–hermitian operators and also differ from those obtained by means of complex–scaling transformations. As an example, Coulomb–like potentials are studied.

Keywords: Factorization method, Gamow vectors, Non–hermitian Hamiltonians.

Resumen

El método de factorización es extendido al caso complejo para construir Hamiltonianos no Hermitianos con espectro real. Algunos de los nuevos Hamiltonianos admiten además un eigenvalor complejo con eigenfunción normalizada. Las funciones de transformación usadas son funciones de Gamow. Los nuevos Hamiltonianos no son pseudo–hermitianos y son diferentes también de aquellos obtenidos con el método de dilatación compleja. Se presenta el caso de potenciales Coulombianos como ejemplo.

Descriptores: Método de factorización, vectores de Gamow, Hamiltonianos no Hermitianos.

PACS: 03.65.Ca; 03.65.Ge; 03.65.Fd

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Acknowledgements

The author is grateful to the organizers of the V Taller de la DGFM–SMF, Morelia Michoacán, México, for the kind invitation. Special thanks are due to U. Nucamendi for the warm hospitality. The author is indebted to M. Lomeli for the manuscript's typing. The support of CONACyT is acknowledged.

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