Adjoint Problem Of Non-self-Adjoint Dirac Eigenvalue Problem

The self-adjointness of Dirac eigenvalue problem determined by its border condition. By virtue of eigenvalue problem and its adjoint problem, we can obtain a sufficient and essential condition to judge the self-adjointness of Dirac eigenvalue problem. Besides, by giving a Dirac eigenvalue problem example and studying the eigenvalue and eigenfunction of it and its adjoint problem, we can obtain an eigenfunction expansion theorem.