One-dimensional q-Dirac equation


Allahverdiev B. , Tuna H.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.40, no.18, pp.7287-7306, 2017 (Journal Indexed in SCI) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 18
  • Publication Date: 2017
  • Doi Number: 10.1002/mma.4529
  • Title of Journal : MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Page Numbers: pp.7287-7306

Abstract

In this paper, we introduce a q-analog of 1-dimensional Dirac equation. We investigate the existence and uniqueness of the solution of this equation. Later, we discuss some spectral properties of the problem, such as formally self-adjointness, the case that the eigenvalues are real, orthogonality of eigenfunctions, Green function, existence of a countable sequence of eigenvalues, and eigenfunctions forming an orthonormal basis of L-q(2)((0, a); E). Finally, we give some examples.