Levinson's theorem for the Schrödinger equation in one dimension

DOI10.1023/A:1003604830131zbMath0968.81008arXivquant-ph/9903016MaRDI QIDQ1580725

Shi-Hai Dong, Zhong-Qi Ma

Publication date: 17 September 2001

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/9903016

zbMATH Keywords

phase shiftsymmetric potentialLevinson's theoremSturm-Liouville theoremnumber of bound statesone-dimensional Schrödinger equationdecays at infinity faster than \(x^{-2}\)even (odd) parityfinite zero-energy solution

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Sturm-Liouville theory (34B24) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) (S)-matrix theory, etc. in quantum theory (81U20)

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Quantum anomaly and thermodynamics of one-dimensional fermions with antisymmetric two-body interactions

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