Relativistic one-dimensional hydrogen atom

Abstract

Equivalence between focused paraxial beams and the quantum harmonic oscillator Am. J. Phys. 73, 625 (2005) Elementary Quantum Mechanics in One Dimension Am. J. Phys. 73, 480 (2005) The wave function and reality Am. J. Phys. 73, 197 (2005) Quantum harmonic oscillator revisited: A Fourier transform approach Am.

Energy spectrum of a relativistic two-dimensional hydrogen-like atom in a constant magnetic field of arbitrary strength

“…The results obtained after solving the Klein-Gordon equation apply to an electron without spin. The advantage of this approach [15] can be easily understood if we recall that the Schödinger equation does not take into account the spin of the electron (1) and then we can directly compare the relativistic and nonrelativistic energy spectra.…”

“…A less studied problem is that of a relativistic 2D hydrogen atom in a magnetic field. Perhaps relativistic effects are not very important in semi-conducting devices but nevertheless they cannot be neglected when the interacting potentials are strong [14,15]. Recently, the importance of considering relativistic effects has been pointed out when one computes the energy levels of semiconductors in high magnetic fields [16].…”

One-dimensional Coulomb problem in Dirac materials

“…The analogous relativistic problem [12][13][14], as governed by Dirac's equation, is equally fascinating, and likewise, the problem has also been investigated in low dimensions, both in two dimensions [15,16] and in one dimension [17][18][19]. The rise of Dirac materials [20], condensed matter systems with quasiparticles welldescribed by the Dirac equation, has led to revisits of Dirac-Kepler problems with Dirac-like matrix Hamiltonians.…”

On Duffin–Kemmer–Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound-states for the one-dimensional inversely linear background

“…This problem was also analyzed with the Klein-Gordon equation for a Lorentz vector coupling. 24,25 By using the technique of continuous dimensionality, the problem was approached with the Schrödinger, Klein-Gordon, and Dirac equations. 26 In this last work, it was concluded that the Klein-Gordon equation, with the interacting potential considered as a time component of a vector, provides unacceptable solutions while the Dirac equation has no bounded solutions at all.…”