Noncentral Potentials: The Generalized Levinson Theorem and the Structure of the Spectrum

Newton, R.G.

doi:10.1063/1.523428

Noncentral Potentials: The Generalized Levinson Theorem and the Structure of the Spectrum

R.G. Newton
(
- Indiana U.
)

1977

10 pages

Published in:

J.Math.Phys. 18 (1977) 1348-1357

DOI:

10.1063/1.523428

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Abstract: (AIP)

Fredholm theory is applied to the Lippmann–Schwinger equation for noncentral potentials. For a specified wide class of potentials it is proved that the modified Fredholm determinant cannot vanish for real k≠0. The point k=0 is examined and the analog of the distinction between zero‐energy bound states and zero‐energy resonances for central potentials is found. A generalized Levinson theorem is proved.

QUANTUM MECHANICS: POTENTIAL SCATTERING
POTENTIAL: ANALYTIC PROPERTIES
ENERGY SPECTRUM: BOUND STATE
S-MATRIX
UNITARITY

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