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A uniqueness theorem for higher order anharmonic oscillators

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We study for alpha is an element of R, k is an element of N \ {0} the family of self-adjoint operators

-d(2)/dt(2) + (t(k+1)/k+1 - alpha)(2)

in L-2(R) and show that if k is even then alpha = 0 gives the unique minimum of the lowest eigenvalue of this family of operators. Combined with earlier results this gives that for any k >= 1, the lowest eigenvalue has a unique minimum as a function of alpha.

OriginalsprogEngelsk
TidsskriftJournal of Spectral Theory
Vol/bind5
Nummer2
Sider (fra-til)235-249
Antal sider15
ISSN1664-039X
DOI
StatusUdgivet - 2015

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