The Expansion Theorem For The Eigenvalue Problem Of The Coupling Dirac Equation With Periodic Boundary Conditions

Let where real function I,m,p,q,r,s∈C2[0,π.The following problem is called eigenvalue problem of the coupling4×4Dirac equation under periodic boundary condition: The eigenfunction expansion theorem of this eigenvalue problem is proved on this paper. First by means of complex analysis the entire ω(λ) is obtained, whose zero set coincides with the set of the corresponding eigenvalue problem. And then a corresponding self-adjiont and compact operator be found. Finally the expansion theorem be proved by the methods of functionai analysis.