Discreteness conditions of the spectrum of Schroedinger operators

Journal Article · Sat Jul 01 04:00:00 EDT 1978 · J. Math. Anal. Appl.; (United States)

DOI:https://doi.org/10.1016/0022-247X(78)90013-6· OSTI ID:5332776

Benci, V ^[1]; Fortunato, D

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1. Inst. di Matematiche Applicate, Pisa, Italy

The spectral properties of Schroedinger operators H = -..delta.. + V(x) (..delta.. is the Laplacian and V, a potential) are studied. V is assumed positive and ..integral../sub S(x/(1/V(y))dy ..-->.. 0 for abs. value (x) ..-->.. + infinity, where S(x) is the unit sphere centered at x. It is proved that the spectrum, sigma(h), of the self-adjoint realization, h, of H in L/sup 2/ (R/sub n/) is discrete, i.e., sigma(h) consists of a denumerable set of eigenvalues of finite multiplicity. The proof of this theorem is based on the compact embedding of a suitable Sobolev weighted space into L/sup 2/(R/sub n/). (RWR)

• OSTI ID: 5332776
• Journal Information: J. Math. Anal. Appl.; (United States), Journal Name: J. Math. Anal. Appl.; (United States) Vol. 64:3; ISSN JMANA
• Country of Publication: United States
• Language: English

Related Subjects

658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EIGENVALUES
EQUATIONS
LAPLACIAN
MATHEMATICAL OPERATORS
QUANTUM OPERATORS
SCHROEDINGER EQUATION
WAVE EQUATIONS