Exact analytical solutions of a two-dimensional hydrogen atom in a constant magnetic field

2017 ◽  
Vol 58 (4) ◽  
pp. 042102 ◽  
Author(s):  
Dai-Nam Le ◽  
Ngoc-Tram D. Hoang ◽  
Van-Hoang Le
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Analytical Solutions ◽  
Constant Magnetic Field ◽  
Two Dimensional ◽  
Exact Analytical Solutions

Visco-resistive magnetic reconnection due to steady inertialess flows. Part 1. Exact analytical solutions

1997 ◽  
Vol 348 ◽  
pp. 327-347 ◽  
Author(s):  
VYACHESLAV S. TITOV ◽  
E. R. PRIEST
Keyword(s):  
Magnetic Field ◽  
Magnetic Reconnection ◽  
Current Density ◽  
Analytical Solutions ◽  
Wide Class ◽  
Current Density Distribution ◽  
Two Dimensional ◽  
Exact Analytical Solutions ◽  
Strong Current ◽  
The Ideal

Magnetic reconnection at an X-type neutral point of a two-dimensional magnetic field is studied in an incompressible viscous resistive fluid whose flow is assumed to be slow enough that its inertia is negligible. In both the ideal and resistive magnetohydrodynamic approximations current singularities appear at the X-point and along the separatrices. It is shown here analytically that the combined effect of viscosity and resistivity can resolve these singularities with the flow crossing the separatrices. A wide class of exact solutions describing the structure of the flow and current density distribution is found. The results suggest that reconnection may occur with localized distributions of strong current density restricted to finite regions.

scholarly journals THE ENERGY EIGENVALUES OF THE TWO DIMENSIONAL HYDROGEN ATOM IN A MAGNETIC FIELD

2006 ◽  
Vol 15 (06) ◽  
pp. 1263-1271 ◽  
Author(s):  
A. SOYLU ◽  
O. BAYRAK ◽  
I. BOZTOSUN
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Iteration Method ◽  
Weak Magnetic Field ◽  
The Other ◽  
Asymptotic Iteration Method ◽  
Iterative Approach ◽  
Two Dimensional ◽  
Energy Eigenvalues ◽  
The Magnetic Field

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the case with no magnetic field analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for n=2-10 and m=0-1 states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.

Two-dimensional hydrogen atom in a strong magnetic field

2003 ◽  
Vol 36 (29) ◽  
pp. 7923-7951 ◽  
Author(s):  
Marko Robnik ◽  
Valery G Romanovski
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Strong Magnetic Field ◽  
Two Dimensional

Highly accurate analytical energy of a two-dimensional exciton in a constant magnetic field

2016 ◽  
Vol 495 ◽  
pp. 16-20 ◽  
Author(s):  
Ngoc-Tram D. Hoang ◽  
Duy-Anh P. Nguyen ◽  
Van-Hung Hoang ◽  
Van-Hoang Le
Keyword(s):  
Magnetic Field ◽  
Constant Magnetic Field ◽  
Two Dimensional
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