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

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.

References in corpus (10)

• Charge accumulation at the boundaries of a graphene strip induced by a gate voltage: Electrostatic approach
• The Woods-Saxon Potential in the Dirac Equation
• Exact solution of the Schrödinger equation for the inverse square root potential $V_0/\sqrt{x}$
• Solutions of the bi-confluent Heun equation in terms of the Hermite functions
• Schrödinger potentials solvable in terms of the general Heun functions
• The conditionally exactly solvable potentials: A misunderstanding (comment on "Conditionally exactly soluble class of quantum potentials")
• Discretization of Natanzon potentials
• Maslov index for power-law potentials
• Comment on "Fun and frustration with quarkonium in a 1+1 dimension," by R. S. Bhalerao and B. Ram [Am. J. Phys. 69 (7), 817-818 (2001)]
• Nodal theorems for the Dirac equation in d >= 1 dimensions

Cited by in corpus (3)

• Dirac Hamiltonian in a supersymmetric framework
• Position-dependent mass Dirac equation and local Fermi velocity
• So (2, 1) algebra, local Fermi velocity, and position-dependent mass Dirac equation