The Infinite Square Well with a Point Interaction: A Discussion on the Different Parametrizations
| Autor: | S. González-Martín, F. H. Maldonado-Villamizar, María Ángeles García-Ferrero, Manuel Gadella |
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| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Physics
High Energy Physics - Theory Pure mathematics Physics and Astronomy (miscellaneous) General Mathematics FOS: Physical sciences Dirac delta function Perturbation (astronomy) Mathematical Physics (math-ph) Kinematics Particle in a box Boundary values Hermitian matrix symbols.namesake Operator (computer programming) High Energy Physics - Theory (hep-th) symbols Self-adjoint operator Mathematical Physics |
| Popis: | 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 $K=-d^2/dx^2$ 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 $a\delta(x)+b\delta'(x)$, 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 $a\delta(x)+b\delta'(x)$ can be fixed and determined using the first approach. Comment: 13 pages, 1 figure |
| Databáze: | OpenAIRE |
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