Counting spectrum via the Maslov index for one dimensional θ−periodic schrÖdinger operators

Christopher K.R.T. Jones, Yuri Latushkin, Selim Sukhtaiev

Research output: Contribution to journalArticle

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Abstract

We study the spectrum of the Schrödinger operators with n × n matrix valued potentials on a finite interval subject to θ−periodic boundary conditions. For two such operators, corresponding to different values of θ, we compute the difference of their eigenvalue counting functions via the Maslov index of a path of Lagrangian planes. In addition we derive a formula for the derivatives of the eigenvalues with respect to θ in terms of the Maslov crossing form. Finally, we give a new shorter proof of a recent result relating the Morse and Maslov indices of the Schrödinger operator for a fixed θ.

LanguageEnglish (US)
Pages363-377
Number of pages15
JournalProceedings of the American Mathematical Society
Volume145
Issue number1
DOIs
StatePublished - Jan 1 2017

Fingerprint

Maslov Index
Schrödinger Operator
Mathematical operators
Counting
Boundary conditions
Derivatives
Eigenvalue
Morse Index
Counting Function
Periodic Boundary Conditions
Derivative
Path
Interval
Operator
Form

Keywords

  • Differential operators
  • Discrete spectrum
  • Eigenvalues
  • Hamiltonian systems
  • Schrödinger equation
  • Stability

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Counting spectrum via the Maslov index for one dimensional θ−periodic schrÖdinger operators. / Jones, Christopher K.R.T.; Latushkin, Yuri; Sukhtaiev, Selim.

In: Proceedings of the American Mathematical Society, Vol. 145, No. 1, 01.01.2017, p. 363-377.

Research output: Contribution to journalArticle

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