Eigenvalue Spectrum of a Dirac Particle in Static and Spherical Complex Potential.pdf

a r X i v : q u a n t - p h / 0 3 0 9 1 1 6 v 1 1 5 S e p 2 0 0 3 Eigenvalue Spectrum of a Dirac Particle in Static and Spherical Complex Potential Khaled Saaidi1 Department of Science, University of Kurdistan, Pasdaran Ave., Sanandaj, Iran Institute for Studies in Theoretical Physics and Mathematics, P.O.Box, 19395-5531, Tehran, Iran Keywords: Complex potential, non-Hermitian, Dirac equation, energy spectrum. Abstract It has been observed that a quantum theory need not to be Hermitian to have a real spectrum. We study the non-Hermitian relativistic quantum theories for many com- plex potentials, and we obtain the real relativistic energy eigenvalues and corresponding eigenfunctions of a Dirac charged particle in complex static and spherically symmetric po- tentials. Complex Dirac-Eckart, complex Dirac-Rosen-Morse II, complex Dirac-Scarf and complex Dirac-Poschl-Teller potential are investigated. 1E-mail-1 : KSaaidi@ipm.ir E-mail-2: ksaaidi@uok.ac.ir 1 1 Introduction The first interest study in the non-Hermitian quantum theory date back to an old paper by Caliceti et al [1]. The imaginary cubic oscillator problem in the context of perturbation theory has been studied in [1]. The energy spectrum of that model is real and discrete. It shows that one may construct many new Hamiltonians that have real spectrum, although, their Hamilto- nians are not Hermitian. The key idea of the new formalism (non-Hermitian quantum theory) lies in the empirical observation that the existence of the real spectrum need not to necessarily be attributed to the Hermiticity of the Hamiltonian. Such non-Hermitian formalism, for the context of Schro?dinger Hamiltonian have been studied for several models in [1-25]. The analysis of the related purely real spectra of energies has been performed with different techniques. For example, resummations of divergent perturbation series[1], delta expansions [2], WKB method [6], functional analysis [8], pseudo-Hermitian methods [17, 21, 23], and com