Integral Equation Approach for a Hydrogen Atom in a Strong Magnetic Field

The problem of a hydrogen atom in a strong magnetic field is a notorious example of a quantum system that has genuinely different asymptotic behaviors in different directions. In the direction perpendicular to the magnetic field the motion is quadratically confined, while in the direction along the...

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Bibliographic Details
Published inFew-body systems Vol. 65; no. 4; p. 95
Main Authors Carter, B. P., Papp, Z.
Format Journal Article
LanguageEnglish
Published Vienna Springer Vienna 26.10.2024
Springer Nature B.V
Subjects
Asymptotic properties
Atomic
Hadrons
Hamiltonian functions
Heavy Ions
Hilbert space
Hydrogen atoms
Integral equations
Magnetic fields
Molecular
Nuclear Physics
Operators (mathematics)
Optical and Plasma Physics
Particle and Nuclear Physics
Physics
Physics and Astronomy
Quantum theory
Subsystems
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Summary:The problem of a hydrogen atom in a strong magnetic field is a notorious example of a quantum system that has genuinely different asymptotic behaviors in different directions. In the direction perpendicular to the magnetic field the motion is quadratically confined, while in the direction along the field line the motion is a Coulomb-distorted free motion. In this work, we identify the asymptotically relevant parts of the Hamiltonian and cast the problem into a Lippmann-Schwinger form. Then, we approximate the asymptotically irrelevant parts by a discrete Hilbert space basis that allows an exact analytic evaluation of the relevant Green’s operators by continued fractions. The total asymptotic Green’s operator is calculated by a complex contour integral of subsystem Green’s operators. We present a sample of numerical results for a wide range of magnetic field strengths.
ISSN:1432-5411
0177-7963
1432-5411
DOI:10.1007/s00601-024-01969-3