Variational approach to a hydrogen atom in a uniform magnetic field of arbitrary strength

2000/05/17 by M. Bachmann, Michael Bachmann, H. Kleinert +2 · 13 citations
Mathematics · Physics and Astronomy · #Atom (system on chip) #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Electron #Feynman diagram #Hydrogen #Hydrogen atom #Limit (mathematics) #Logarithm #Magnetic field #Mathematical analysis #Mathematics #Physics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Quantum, superfluid, helium dynamics #Variational method #quant-ph

paper · pdf · doi:10.1103/physreva.62.052509

published in Physical Review A 62(5) (American Physical Society) · Author Information under this http://www.physik.fu-berlin.de/~kleinert/institution.html Latest update of paper also at this http://www.physik.fu-berlin.de/~kleinert/307

arxiv created 2000/05/17 · openalex publication_date 2000/10/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Extending the Feynman-Kleinert variational approach, we calculate the temperature-dependent effective classical potential governing the quantum statistics of a hydrogen atom in a uniform magnetic field at all temperatures. The zero-temperature limit yields the binding energy of the electron, which is quite accurate for all magnetic-field strengths, and exhibits, in particular, correct logarithmic growth at large fields.

Citations

• Generating functionals for harmonic expectation values of paths with fixed end points: Feynman diagrams for nonpolynomial interactions
• Effective classical partition functions
• Smearing formula for higher-order effective classical potentials
• Ground states of H, He,…, Ne, and their singly positive ions in strong magnetic fields: The high-field regime
• Variational perturbation theory for density matrices