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International Journal of Theoretical Physics

, Volume 53, Issue 5, pp 1614–1627 | Cite as

The Infinite Square Well with a Point Interaction: A Discussion on the Different Parameterizations

  • M. Gadella
  • M. A. García-Ferrero
  • S. González-Martín
  • F. H. Maldonado-Villamizar
Article

Abstract

The construction of Dirac delta type potentials has been achieved with the use of the theory of self adjoint extensions of non-self adjoint formally Hermitian (symmetric) operators. The application of this formalism to investigate the possible self adjoint extensions of the one dimensional kinematic operator \(K=-\frac{d^{2}}{dx^{2}}\) on the infinite square well potential is quite illustrative and has been given elsewhere. This requires the definition and use of four independent real parameters, which relate the boundary values of the wave functions at the walls. By means of a different approach, that fixes matching conditions at the origin for the wave functions, it is possible to define a perturbation of the type (x)+′(x), thus depending on two parameters, on the infinite square well. The objective of this paper is to investigate whether these two approaches are compatible in the sense that perturbations like (x)+′(x) can be fixed and determined using the first approach.

Keywords

Point potentials Parameterizations of self adjoint extensions 

Notes

Acknowledgement

Financial support is acknowledged to the Ministry of Economy and Innovation of Spain through the Grant MTM2009-10751.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • M. Gadella
    • 1
  • M. A. García-Ferrero
    • 1
  • S. González-Martín
    • 1
  • F. H. Maldonado-Villamizar
    • 2
  1. 1.Department of Theoretical, Atomic Physics and Optics, Facultad de CienciasUniversity of ValladolidValladolidSpain
  2. 2.Departamento de FísicaCentro de Investigación y Estudios Avanzados del IPNMéxico DFMexico

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