On Minimal Entire Solutions of the One-Dimensional Difference Schrödinger Equation with the Potential υ(z) = e −2πiz

Research output

1 Citation (Scopus)

Abstract

Let z ∈ ℂ be a complex variable, and let h ∈ (0, 1) and p ∈ ℂ be parameters. For the equation ψ(z + h) + ψ(z − h) + e −2πiz ψ(z) = 2 cos(2πp)ψ(z), solutions having the minimal possible growth simultaneously as Im z → ∞ and as Im z → − ∞ are studied. In particular, it is shown that they satisfy one more difference equation ψ(z + 1) + ψ(z − 1) + e −2πiz/h ψ(z) = 2 cos(2πp/h)ψ(z).

Original languageEnglish
Pages (from-to)750-761
Number of pages12
JournalJournal of Mathematical Sciences
Volume238
Issue number5
Early online date1 Apr 2019
DOIs
Publication statusPublished - 7 May 2019

Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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