Does Levinson’s theorem count complex eigenvalues?
Copyright policy )Does Levinson’s theorem count complex eigenvalues?
Yes it does ! Indeed an extended version of Levinson's theorem is proposed for a system involving complex eigenvalues. The perturbed system corresponds to a realization of the Schroedinger operator with inverse square potential on the half-line, while the Dirichlet Laplacian on the half-line is chosen for the reference system. The resulting relation is an equality between the number of eigenvalues of the perturbed system and the winding number of the scattering system together with additional operators living at 0-energy and at infinite energy.
10 pages
- Nagoya University Japan
- Claude Bernard University Lyon 1 France
- Laboratoire de Mathématiques Jean Leray France
- University of Lyon System France
- Nagoya University Japan
\(2\)-body potential quantum scattering theory, Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), FOS: Physical sciences, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, Mathematical Physics (math-ph), 530, 510, Nonselfadjoint operator theory in quantum theory including creation and destruction operators, Mathematics - Spectral Theory, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], FOS: Mathematics, Spectral Theory (math.SP), Levinson's theorem, Mathematical Physics, [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP]
\(2\)-body potential quantum scattering theory, Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), FOS: Physical sciences, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, Mathematical Physics (math-ph), 530, 510, Nonselfadjoint operator theory in quantum theory including creation and destruction operators, Mathematics - Spectral Theory, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], FOS: Mathematics, Spectral Theory (math.SP), Levinson's theorem, Mathematical Physics, [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP]
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