The Energy Eigenvalues of the Two Dimensional Hydrogen Atom in a Magnetic Field

Abstract

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 no magnetic field case 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.

13 pages and 5 tables

References in corpus (7)

• Asymptotic iteration method for eigenvalue problems
• Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method
• Asymptotic Iteration Method Solutions to the Relativistic Duffin-Kemmer-Petiau Equation
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• Energy Spectrum of a Relativistic Two-dimensional Hydrogen-like Atom in a Constant Magnetic Field of arbitrary strength
• Analytic computation of the energy levels of a two-dimensional hydrogenic donor in a constant magnetic field
• Scaled variational computation of the energy spectrum of a two-dimensional hydrogenic donor in a magnetic field of arbitrary strength

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• Two Electrons in a Quantum Dot: A Unified Approach
• Anisotropic Features of the Two-dimensional Hydrogen Atom in a Magnetic Field
• Influence of tilted magnetic field on excited states of the two-dimensional hydrogen atom
• Two-dimensional Hydrogen-like Atom in a Constant Magnetic Field
• Relativistic two-dimensional hydrogen-like atom in a weak magnetic field