L2 series solution of the relativistic Dirac-Morse problem for all energies

Details L2 series solution of the relativistic Dirac-Morse problem for all energies L2 series solution of the relativistic Dirac-Morse problem for all energies

2004-05-03

arxiv.org/abs/math-ph/0405008v1

Phys. Lett. A 326.1-2 (2004) 58-69

Physics

Mathematical Physics

13 pages

Scientific paper

We obtain analytic solutions for the one-dimensional Dirac equation with the Morse potential as an infinite series of square integrable functions. These solutions are for all energies, the discrete as well as the continuous. The elements of the spinor basis are written in terms of the confluent hypergeometric functions. They are chosen such that the matrix representation of the Dirac-Morse operator for continuous spectrum (i.e., for scattering energies larger than the rest mass) is tridiagonal. Consequently, the wave equation results in a three-term recursion relation for the expansion coefficients of the wavefunction. The solution of this recursion relation is obtained in terms of the continuous dual Hahn orthogonal polynomials. On the other hand, for the discrete spectrum (i.e., for bound states with energies less than the rest mass) the spinor wave functions result in a diagonal matrix representation for the Dirac-Morse Hamiltonian.

Affiliated with

Also associated with

No associations

Rating

L2 series solution of the relativistic Dirac-Morse problem for all energies does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with L2 series solution of the relativistic Dirac-Morse problem for all energies, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and L2 series solution of the relativistic Dirac-Morse problem for all energies will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-346393