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arXiv · 1912.00430

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

A. M. Ishkhanyan
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Abstract

We present the exact solution of the 1D Dirac equation for the inverse-square-root potential $1/\sqrt{x}$ 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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A. M. Ishkhanyan. 2019-12-01. Exact solution of the 1D Dirac equation for the inverse-square-root potential $1/\sqrt{x}$. https://doi.org/10.1515/zna-2020-0083

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