Something new about radial wave functions of fermions in the repulsive Coulomb field

Abstract

An impermeable barrier at $r=r_{cl}$ in the effective potential of the relativistic Schrödinger-type equation leads to exclusion of the range $0\le r<r_{cl}$ from the wave function domain. Based on duality of the Schrödinger-type equation and the Dirac equation, a similar exclusion should be made in the wave functions domain of the Dirac equation. As a result, we obtain new solutions to the Dirac equation in the Coulomb repulsive field. Calculations show that depending on working parameters, at distances of several fractions or units of the Compton wavelength of the fermion from $r=r_{cl}$ new solutions almost coincide with the standard Coulomb functions of the continuous spectrum. Practically, matrix elements with new solutions will coincide to a good accuracy with standard matrix elements with the Coulomb functions of the continuous spectrum. Our consideration is methodological and helpful for discussing further development of quantum theory.

21 pages, 11 figures

References in corpus (5)

• Position and spin in relativistic quantum mechanics
• Quantum mechanics of stationary states of particles in a space-time of classical black holes
• Second-order stationary solutions for fermions in an external Coulomb field
• Quantum electrodynamics with self-conjugated equations with spinor wave functions for fermion fields
• The lack of vacuum polarization in quantum electrodynamics with spinors in fermion equations

Cited by in corpus (1)

• Prüfer transformation and its application to the numerical description of the motion of quantum particles with various spins in the fields of classical black holes