Paper Info
Title
High-accuracy numerical calculations of the bound states of a hydrogen atom in a constant magnetic field with arbitrary strength
Abstract
We develop a simple and effective method for solving the Schrödinger equation of a hydrogen atom in a constant magnetic field with arbitrary strength. Energies are obtained not only for the ground and low-lying states but also for highly excited states with precision from 12 up to 20 decimal digits. The calculations are performed for an entire range of magnetic field intensity up to 9.4×108 Tesla, the strongest field ever observed. The strong point of the development of the method is the construction of an anharmonic oscillator model for a hydrogen atom in a constant magnetic field via the Kustaanheimo–Stiefel transformation. This model allows the use of purely algebraic calculations and the Feranchuk–Komarov (FK) operator method for effectively solving the Schrödinger equation. The advantages of the basis set in this work are also discussed to extend its application to other problems, such as multi-electron atoms in a constant magnetic field. We also provide a program written by FORTRAN for the solutions mentioned above.
Year
DOI
Venue
2019
10.1016/j.cpc.2019.02.013
Computer Physics Communications
Keywords
Field
DocType
Hydrogen atom,Magnetic field,High-accuracy numerical solutions,The FK operator method,Harmonic oscillator model,The Kustaanheimo–Stiefel transformation
Linear algebra,Algebraic number,Subroutine,Matrix (mathematics),Mathematical analysis,Schrödinger equation,Operator (computer programming),Harmonic oscillator,Mathematics,Free parameter
Journal
Volume
ISSN
Citations 
240
0010-4655
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Thanh-Xuan H. Cao100.34
Duy-Nhat Ly200.34
Ngoc-Tram D. Hoang300.34
Van-Hoang Le410.69