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Register a new userVariational proof of the existence of eigenvalues for star graphs
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Added by
Konstantin Pankrashkin
Publication date
2015
fields
Physics
and research's language is
English
Authors
Konstantin Pankrashkin
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We provide a purely variational proof of the existence of eigenvalues below the bottom of the essential spectrum for the Schrodinger operator with an attractive $delta$-potential supported by a star graph, i.e. by a finite union of rays emanating from the same point. In contrast to the previous works, the construction is valid without any additional assumption on the number or the relative position of the rays. The approach is used to obtain an upper bound for the lowest eigenvalue.
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