Asymptotic iteration method solution of the energy spectrum of two-dimensional screened donor in a magnetic field

2008 ◽  
Vol 40 (3) ◽  
pp. 443-448 ◽  
Author(s):  
A. Soylu ◽  
I. Boztosun
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Iteration Method ◽  
Asymptotic Iteration Method ◽  
Two Dimensional

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.

EXAMINATION OF $V(r) = -\frac{Z}{r} + gr +\lambda r^2$ POTENTIAL IN THE PRESENCE OF MAGNETIC FIELD

2010 ◽  
Vol 19 (07) ◽  
pp. 1349-1356 ◽  
Author(s):  
M. AYGUN ◽  
Y. SAHIN ◽  
I. BOZTOSUN
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Iteration Method ◽  
Weak Magnetic Field ◽  
Asymptotic Iteration Method ◽  
Two Dimensional ◽  
Strong Magnetic Fields ◽  
Energy Eigenvalues ◽  
Alternative Approach ◽  
Radial Schrödinger Equation

We present an alternative approach, the asymptotic iteration method, to solve the two-dimensional radial Schrödinger equation for [Formula: see text] potential in a magnetic field. The energy eigenvalues for arbitrary Larmor frequencies ranging from ωL = 0.1 to 10.0 are obtained and the results are compared with the nonmagnetic field case, ωL = 0, in order to show the effect of the presence of the weak and strong magnetic fields on the energy eigenvalues. It is shown that the method presented in this paper provides the energy eigenvalues in a systematic way not only in the weak magnetic field but also in the strong magnetic field regions with any Larmor frequencies.

Energy spectrum for two-dimensional periodic potentials in a magnetic field

1993 ◽  
Vol 47 (19) ◽  
pp. 13019-13022 ◽  
Author(s):  
O. Kühn ◽  
V. Fessatidis ◽  
H. L. Cui ◽  
P. E. Selbmann ◽  
N. J. M. Horing
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Two Dimensional ◽  
Periodic Potentials

scholarly journals ENERGY SPECTRUM OF THE GROUND STATE OF A TWO-DIMENSIONAL RELATIVISTIC HYDROGEN ATOM IN THE PRESENCE OF A CONSTANT MAGNETIC FIELD

2003 ◽  
Vol 17 (25) ◽  
pp. 1331-1341 ◽  
Author(s):  
VÍCTOR M. VILLALBA ◽  
RAMIRO PINO
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Ground State ◽  
Constant Magnetic Field ◽  
Two Dimensional ◽  
Relativistic Limit ◽  
Dirac Electron ◽  
Relativistic Hydrogen ◽  
Relativistic Hydrogen Atom ◽  
The Magnetic Field

We compute the energy spectrum of the ground state of a 2D Dirac electron in the presence of a Coulomb potential and a constant magnetic field perpendicular to the plane where the the electron is confined. With the help of a mixed-basis variational method we compute the wave function and the energy level and show how it depends on the magnetic field strength. We compare the results with those obtained numerically as well as in the non-relativistic limit.

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