Exact solution of the 1D Dirac equation for the inverse-square-root potential $1/\sqrt{x}$
Quantum Physics
2020-09-04 v3
Abstract
We present the exact solution of the 1D Dirac equation for the inverse-square-root potential for several configurations of vector, pseudo-scalar and scalar fields. Each fundamental solution of the problem can be written as an irreducible linear combination of two Hermite functions of a scaled and shifted argument. We derive the exact equations for bound-state energy eigenvalues and construct accurate approximations for the energy spectrum.
Keywords
Cite
@article{arxiv.1912.00430,
title = {Exact solution of the 1D Dirac equation for the inverse-square-root potential $1/\sqrt{x}$},
author = {A. M. Ishkhanyan},
journal= {arXiv preprint arXiv:1912.00430},
year = {2020}
}