scholarly journals Numerical solutions of the Maung-Norbury-Kahana equation with the coulomb potential in momentum space

2017 ◽  
Vol 64 (1) ◽  
pp. 8 ◽  
Author(s):  
Jiao-Kai Chen
Keyword(s):  
Coulomb Potential ◽  
Momentum Space ◽  
Bound States ◽  
Numerical Solutions ◽  
Complicated Form

In this paper, the numerical solutions of the Maung-Norbury-Kahana equation which has the complicated form of the eigenvalues are presented. Taken as examples, the bound states $e^+e^-$, $\mu^+\mu^-$ and $\mu^+e^-$ are discussed by employing the Maung-Norbury-Kahana equation with the Coulomb potential.

scholarly journals Study in momentum space of phase-dependent effects on ionization of hydrogen atom interacting with short infrared laser pulses

2021 ◽  
Author(s):  
Fréderic ONGONWOU ◽  
Hugues Merlain TETCHOU ◽  
Thierry Blanchard EKOGO ◽  
Bakari ABDOURAMAN ◽  
Moïse Godefroy KWATO
Keyword(s):  
Laser Pulse ◽  
Coulomb Potential ◽  
Momentum Space ◽  
Bound States ◽  
Laser Pulses ◽  
Infrared Laser ◽  
Time Dependent ◽  
Basis Set ◽  
Angular Distributions ◽  
Carrier Envelope Phase

We examine above-threshold ionization spectra of model atomic hydrogen in short infrared laser pulses by solving the one-electron time-dependent Schr\“odinger equation in momentum space. To bypass the difficulty of solving the time-dependent Schr\”odinger equation with the interacting nonlocal Coulomb potential, we have recently formulated an alternative \emph{ab initio} approach [Ongonwou et al. Annals of Physics {\bf 375}, 471 (2016)], which is relied on the expansion of the atomic wavefunction and the interacting nonlocal Coulomb potential on a discrete basis set of Coulomb Sturmians in momentum space. As far as short infrared laser pulses are concerned, we have numerically evaluated the photoelectron momentum distributions, angular distributions and bound states populations. The results obtained from our accurate new computationally method are compared against predictions of other time-dependent calculations in the literature. This new theoretical model shows its sensitivity to the carrier-envelope phase of the laser pulse and captures the left-right dependence of the emitted photoelectrons momentum and angular distributions. More precisely, short pulses manifest significant dependence of the differential ionization probability on carrier-envelope phase of the laser pulse and broken forward-backward symmetry in the angular distributions.

scholarly journals The relativistic bound states of Coulomb potential plus a new ring-shaped potential

2006 ◽  
Vol 55 (8) ◽  
pp. 3875
Author(s):  
Chen Chang-Yuan ◽  
Sun Dong-Sheng ◽  
Lu Fa-Lin
Keyword(s):  
Coulomb Potential ◽  
Bound States ◽  
Relativistic Bound States

scholarly journals The spinless relativistic Hellmann problem

2019 ◽  
Vol 34 (05) ◽  
pp. 1950028
Author(s):  
Wolfgang Lucha ◽  
Franz F. Schöberl
Keyword(s):  
Coulomb Potential ◽  
Bound States ◽  
Yukawa Potential ◽  
Equations Of Motion ◽  
Kinetic Term ◽  
Discrete Eigenvalue ◽  
Hellmann Potential ◽  
Relativistic Equations

We compile some easily deducible information on the discrete eigenvalue spectra of spinless Salpeter equations encompassing, besides a relativistic kinetic term, interactions which are expressible as superpositions of an attractive Coulomb potential and an either attractive or repulsive Yukawa potential and, hence, generalizations of the Hellmann potential employed in several areas of science. These insights should provide useful guidelines to all attempts of finding appropriate descriptions of bound states by (semi-)relativistic equations of motion.

scholarly journals QUANTUM ELECTRODYNAMICS OF RELATIVISTIC BOUND STATES WITH CUTOFFS

2004 ◽  
Vol 01 (02) ◽  
pp. 271-314 ◽  
Author(s):  
JEAN-MARIE BARBAROUX ◽  
MOUEZ DIMASSI ◽  
JEAN-CLAUDE GUILLOT
Keyword(s):  
Current Density ◽  
Coulomb Potential ◽  
Ground State ◽  
Quantum Electrodynamics ◽  
Bound States ◽  
Coupling Constants ◽  
Relativistic Electrons ◽  
Small Coupling ◽  
Electrons And Positrons ◽  
Relativistic Bound States

We consider a Hamiltonian with ultraviolet and infrared cutoffs, describing the interaction of relativistic electrons and positrons in the Coulomb potential with photons in Coulomb gauge. The interaction includes both interaction of the current density with transversal photons and the Coulomb interaction of charge density with itself. We prove that the Hamiltonian is self-adjoint and has a ground state for sufficiently small coupling constants.

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