Critical strength of attractive central potentials

2004/11/02 by Fabian Brau, Monique Lassaut
Mathematics · Physics and Astronomy · #Holomorphic and Operator Theory #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1088/0305-4470/37/46/010

published as J. Phys. A37, 11243 (2004) · 18 pages

arxiv created 2004/11/02 · openalex publication_date 2004/11/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We obtain several sequences of necessary and sufficient conditions for the existence of bound states applicable to attractive (purely negative) central potentials. These conditions yield several sequences of upper and lower limits on the critical value, g (ℓ) c , of the coupling constant (strength), g , of the potential, V ( r ) = − gv ( r ), for which a first ℓ-wave bound state appears, which converges to the exact critical value.

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