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The Levinson Theorem for Dirac Equation

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Wave Equations in Higher Dimensions

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Abstract

The Levinson theorem as an important theorem in the quantum scattering theory has been generalized and applied to different fields in modern physics. With the interest of higher-dimensional field theory, the Levinson theorem for the Schrödinger equation in arbitrary D dimensions was studied. The purpose of this Chapter is to establish the Levinson theorem for Dirac equation. We shall first study the generalized Sturm-Liouville theorem, the number of bound states, the Levinson theorem, and then we present the Friedel theorem and comparison theorem due to its close connection with them.

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  1. Escuela Superior de Física y Matemáticas, Unidad Profesional Adolfo López Mateos, Instituto Politécnico Nacional, Edificio 9, Mexico DF, 07738, Mexico

    Shi-Hai Dong

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Dong, SH. (2011). The Levinson Theorem for Dirac Equation. In: Wave Equations in Higher Dimensions. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1917-0_15

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