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 - <p style="text-align: justify;">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.</p>