Exact solution of the 1D Dirac equation for the inverse-square-root potential 1/x$1/\sqrt{x}$

@article{Ishkhanyan2019ExactSO,
  title={Exact solution of the 1D Dirac equation for the inverse-square-root potential 1/x\$1/\sqrt\{x\}\$},
  author={Artur M. Ishkhanyan},
  journal={Zeitschrift f{\"u}r Naturforschung A},
  year={2019},
  volume={75},
  pages={771 - 779}
}
  • A. Ishkhanyan
  • Published 1 December 2019
  • Mathematics, Physics
  • Zeitschrift für Naturforschung A
Abstract We present the exact solution of the 1D Dirac equation for the inverse-square-root potential 1/x$1/\sqrt{x}$ 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. 
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