Non-numerical determination of the number of bound states in some screened Coulomb potentials

Journal Article · Sun Jan 01 04:00:00 EST 1995 · Physical Review A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.51.128· OSTI ID:7065369

Znojil, M ^[1]

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1. Department of Theoretical Nuclear Physics, Institute of Nuclear Physics, Academy of Sciences, 250 68 Rez (Czech Republic)

We construct potentials [ital V][sup [l brace][ital s][ital c][ital r][ital K][r brace]]([ital r]) which support a finite number [ital scrK] of bound states in such a way that the highest normalizable excitation lies precisely at the threshold energy [ital E]=0. We expect that many realistic interactions [ital V][sub (phys)]([ital r]) may be bracketed between these forces due to their flexibility and plausible screened Coulombic form. Thus, we propose an estimate of the number [ital N][sub BS] of bound states in an arbitrary potential [ital V][sub (phys)]([ital r]) via requirements [ital V][sup [l brace]K[sub [ital L]][r brace]][lt][ital V][sub (phys)][ge][ital V][sup [l brace]K[sub [ital U]][r brace]] and subsequent inequalities K[sub [ital L]][gt][ital N][sub BS][ge]K[sub [ital U]]. In particular, we get a strict prediction [ital N][sub BS]=K[sub [ital U]] whenever the bracketing proves tight enough, with K[sub [ital U]][equivalent to]K[sub [ital L]][minus]1.

• OSTI ID: 7065369
• Journal Information: Physical Review A; (United States), Journal Name: Physical Review A; (United States) Vol. 51:1; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
COULOMB FIELD
DIFFERENTIAL EQUATIONS
EIGENSTATES
ELECTRIC FIELDS
ENERGY
ENERGY LEVELS
EQUATIONS
EXCITED STATES
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIAL ENERGY
SCHROEDINGER EQUATION
WAVE EQUATIONS