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The Levinson Theorem for Schrödinger Equation

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Wave Equations in Higher Dimensions

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Abstract

The Levinson theorem as an important theorem in quantum scattering theory establishes the relation between the total number n l of bound states and the phase shift δ l (0) of the scattering states at zero momentum. In this Chapter, we are ready to study the scattering states and bound states of the Schrödinger equation with central potential, the Sturm-Liouville theorem, the establishment of the non-relativistic Levinson theorem, the discussions on the general case. Finally, we shall outline the comparison theorem.

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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 Schrödinger Equation. In: Wave Equations in Higher Dimensions. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1917-0_9

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