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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References

SHOWING 1-10 OF 41 REFERENCES
Quasi-exact solution to the Dirac equation for the hyperbolic-secant potential
We analyze bound modes of two-dimensional massless Dirac fermions confined within a hyperbolic secant potential, which provides a good fit for potential profiles of existing top-gated graphene…
The Woods-Saxon potential in the Dirac equation
The two-component approach to the one-dimensional Dirac equation is applied to the Woods?Saxon potential. The scattering and bound state solutions are derived and the conditions for a transmission…
The Dirac oscillator
Dirac's free particle equation originated in an attempt to express linearly the relativistic quadratic relation between energy and momentum. The authors introduce a Dirac equation which, besides the…
Transmission resonance for a Dirac particle in a one-dimensional Hulthén potential
We have solved exactly the two-component Dirac equation in the presence of a spatially one-dimensional Hulthén potential, and presented the Dirac spinors of scattering states in terms of…
Nodal theorems for the Dirac equation in d ≥ 1 dimensions
A single particle obeys the Dirac equation in d≥1 spatial dimensions and is bound by an attractive central monotone potential that vanishes at infinity. In one dimension, the potential is even, and…
The Dirac Equation and Its' Solutions
The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics, representing the one-particle wave equation of motion for electrons in an external…
Schrödinger potentials solvable in terms of the general Heun functions
Solutions of the bi-confluent Heun equation in terms of the Hermite functions
Schrödinger potentials solvable in terms of the confluent Heun functions
We show that if the potential is proportional to an energy-independent continuous parameter, then there exist 15 choices for the coordinate transformation that provide energy-independent potentials…
Maslov index for power-law potentials
The Maslov index in the semiclassical Bohr–Sommerfeld quantization rule is calculated for one-dimensional power-law potentials V (x) = −V0/xs, x > 0, 0 < s < 2 The result for the potential…
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