Eigenfunction expansion associated with the one-dimensional Schrödinger equation on semi-infinite time scale intervals

Huseynov A.

Reports on Mathematical Physics, vol.66, no.2, pp.207-235, 2010 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 66 Issue: 2
  • Publication Date: 2010
  • Doi Number: 10.1016/s0034-4877(10)00026-1
  • Journal Name: Reports on Mathematical Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.207-235
  • Keywords: Delta and nabla derivatives, Jacobi matrix, Spectral function, Time scale
  • Ankara University Affiliated: Yes

Abstract

We prove the existence of a spectral function (spectral measure or orthogonality measure) for the one-dimensional Schrödinger equation on semi-infinite time scale intervals. A Parseval equality and an expansion formula in eigenfunctions are established in terms of the spectral function. The result obtained unifies and extends the well-known results on the existence of a spectral measure for the one-dimensional Schrödinger operator on the semi-axis and for semi-infinite Jacobi matrices. © 2010 Polish Scientific Publishers PWN, Warszawa.