High Precision Method for Calculating the Energy Values of the Hydrogen Atom in a Strong Magnetic Field
The new method for calculating the energy values of the hydrogen atom in a strong magnetic field (0 ≤ B ≤ 1013 G ) with high degree of accuracy is developed in this paper. The proposed method is based on the Kantorovich method for solving eigenvalue problems. This method successfully reduces the given two dimensional spectral problem for the Schrödinger equation to the spectral problems for one one-dimensional equation and the system of ordinary second-order differential equations. The rate of convergence is examined numerically and is illustrated in the table. The results are in good agreement with the best one up to now and show that 12 significant digits are computed in the obtaining energy values.
KeywordsHydrogen Atom Matrix Element Eigenvalue Problem Element Matrice Radial Equation
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