Volume 5, Issue 3
On Computation for a Hydrogen Atom in Arbitrary Magnetic Fields Using Finite Volume Method

Gyanendra P. Sasmal

J. At. Mol. Sci., 5 (2014), pp. 187-205.

Published online: 2014-05

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  • Abstract

The Schrödinger equation in a 2D cylindrical coordinate system is numerically solved for the ground state and a few excited states of the hydrogen atom in arbitrary magnetic fields. The second order discretization of the PDEs on finite volumes results in a set of algebraic equations that are solved simultaneously using Gauss-Seidel Algebraic Multi-Grid (AMG) solver. The modified Stodola-Vianello method is implemented using Gram-Schmidt orthogonalization process to extract the first few energy states and their wave functions concurrently. A detailed mesh convergence study suggests that both energies and wave functions correctly approach toward the unknown exact solutions.

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@Article{JAMS-5-187, author = {Sasmal , Gyanendra P.}, title = {On Computation for a Hydrogen Atom in Arbitrary Magnetic Fields Using Finite Volume Method}, journal = {Journal of Atomic and Molecular Sciences}, year = {2014}, volume = {5}, number = {3}, pages = {187--205}, abstract = {

The Schrödinger equation in a 2D cylindrical coordinate system is numerically solved for the ground state and a few excited states of the hydrogen atom in arbitrary magnetic fields. The second order discretization of the PDEs on finite volumes results in a set of algebraic equations that are solved simultaneously using Gauss-Seidel Algebraic Multi-Grid (AMG) solver. The modified Stodola-Vianello method is implemented using Gram-Schmidt orthogonalization process to extract the first few energy states and their wave functions concurrently. A detailed mesh convergence study suggests that both energies and wave functions correctly approach toward the unknown exact solutions.

}, issn = {2079-7346}, doi = {https://doi.org/10.4208/jams.110813.021414a}, url = {http://global-sci.org/intro/article_detail/jams/8306.html} }
TY - JOUR T1 - On Computation for a Hydrogen Atom in Arbitrary Magnetic Fields Using Finite Volume Method AU - Sasmal , Gyanendra P. JO - Journal of Atomic and Molecular Sciences VL - 3 SP - 187 EP - 205 PY - 2014 DA - 2014/05 SN - 5 DO - http://doi.org/10.4208/jams.110813.021414a UR - https://global-sci.org/intro/article_detail/jams/8306.html KW - Schrödinger equation, hydrogen atom, magnetic field, finite volume method, eigenvalues, eigenvectors. AB -

The Schrödinger equation in a 2D cylindrical coordinate system is numerically solved for the ground state and a few excited states of the hydrogen atom in arbitrary magnetic fields. The second order discretization of the PDEs on finite volumes results in a set of algebraic equations that are solved simultaneously using Gauss-Seidel Algebraic Multi-Grid (AMG) solver. The modified Stodola-Vianello method is implemented using Gram-Schmidt orthogonalization process to extract the first few energy states and their wave functions concurrently. A detailed mesh convergence study suggests that both energies and wave functions correctly approach toward the unknown exact solutions.

Sasmal , Gyanendra P.. (2014). On Computation for a Hydrogen Atom in Arbitrary Magnetic Fields Using Finite Volume Method. Journal of Atomic and Molecular Sciences. 5 (3). 187-205. doi:10.4208/jams.110813.021414a
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