Generalized Levinson theorem for singular potentials in two dimensions

Journal Article · Tue Jul 01 00:00:00 EDT 2003 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.68.012707· OSTI ID:20639906

Sheka, Denis; Ivanov, Boris; Mertens, Franz G ^[1]

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1. National Taras Shevchenko University of Kiev, 03127 Kiev, (Ukraine)

The Levinson theorem for two-dimensional scattering is generalized for potentials with inverse square singularities. By this theorem, the number of bound states N{sub m}{sup b} in a given mth partial wave is related to the phase shift {delta}{sub m}(k) and the singularity strength of the potential. When the effective potential has an inverse square singularity at the origin of the form {nu}{sup 2}/{rho}{sup 2} and inverse square tail at infinity such as {mu}{sup 2}/{rho}{sup 2}, Levinson's relation gives {delta}{sub m}(0)-{delta}{sub m}({infinity})={pi}[N{sub m}{sup b}+(|{nu}|-|{mu}|)/2].

• OSTI ID: 20639906
• Journal Information: Physical Review. A, Vol. 68, Issue 1; Other Information: DOI: 10.1103/PhysRevA.68.012707; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUND STATE
LEVINSON THEOREM
PARTIAL WAVES
PHASE SHIFT
POTENTIALS
QUANTUM MECHANICS
SCATTERING
SINGULARITY
TWO-DIMENSIONAL CALCULATIONS