One‐dimensional qq ‐Dirac equation

摘要

> 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.