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Spectral properties of a Schrödinger equation with a class of complex potentials and a general boundary condition

✍ Scribed by Gülen Başcanbaz-Tunca

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
206 KB
Volume
286
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper we investigate the spectrum and the spectral singularities of an operator L generalized in L 2 (R + ) by the differential expression

and the boundary condition

where λ is a complex parameter, q k , k = 0, 1, . . . , n -1, are complex valued functions, q 0 , q 1 , . . . , q n-1 are differentiable on (0, ∞), K ∈ L 2 (R + ), and α, β ∈ C with |α| + |β| = 0. Discussing the spectrum we obtain that L has a finite number of eigenvalues and spectral singularities with finite multiplicities if the conditions

hold, where k = 0, 1, . . . , n -1 and ε > 0.

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