The spectral shift function and Levinson's theorem for quantum star graphs

Journal Article · Wed Aug 15 00:00:00 EDT 2012 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4746158· OSTI ID:22093681

Demirel, Semra ^[1]

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1. University of Stuttgart, Department of Mathematics, Pfaffenwaldring 57, D-70569 Stuttgart (Germany)

We consider the Schroedinger operator on a star shaped graph with n edges joined at a single vertex. We derive an expression for the trace of the difference of the perturbed and unperturbed resolvent in terms of a Wronskian. This leads to representations for the perturbation determinant and the spectral shift function, and to an analog of Levinson's formula.

• OSTI ID: 22093681
• Journal Information: Journal of Mathematical Physics, Vol. 53, Issue 8; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DISTURBANCES
GRAPH THEORY
LEVINSON THEOREM
MATHEMATICAL OPERATORS
PERTURBATION THEORY
SCHROEDINGER EQUATION
SPECTRAL FUNCTIONS
SPECTRAL SHIFT