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Bounds on the number of bound states for potentials with critical decay at infinity (1990)

Stubbe, Joachim

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 31 (1990), S. 1177-1180

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: Let V be a potential whose negative part V− decays like c||x||−2 at infinity. If c is not too large, then the Schrödinger operator HV=−Δ+V on Rn, n≥3, has only a finite number of bound states although the associated classical phase space volume is infinite. Optimal conditions are derived for the absence of bound states and a family of bounds on the total number of bound states for the operator HV of the form N0(V)≤ cγ,n ∫Rn (V+c/||x||2)γ− ||x−x0||2γ−n dn x. The basic tool used to obtain results is a family of sharp Sobolev inequalities for the operator A(c)=−Δ−c/||x||2.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.528750

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