The hydrogen atom in the presence of the Fermi-contact interaction

1970/05/01 by A. Velenik, Tomislav P. Živković, Wim H. de Jeu +1 · 1 voice · 2 citations
Chemistry · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced Physical and Chemical Molecular Interactions #Atomic and Molecular Physics

paper · doi:10.1080/00268977000100731

openalex publication_date 1970/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

It is shown that the energy associated with the Fermi-contact part of the hamiltonian of the hydrogen atom cannot be expanded as a perturbation series. A variation calculation shows that the total energy is E 0 when the Fermi-contact operation is added to H 0, and -∞ when it is subtracted. In order to do a priori variational calculations on the ‘second-order’ properties of this operator, such as spin-spin coupling constants, it is probably necessary to remove the singularity caused by the δ function.

Cited by

• Modified delta-function potential for hyperfine interactions
• An exactly solvable model for the Fermi contact interaction

Discussions

• There are two main questions here: a technical question about the "exact" eigenvalues of the Hamiltonian $$ H=-\frac{1}{2m}\sum_{i=1}^D\frac{\partial^2}{\partial x_i^2}+U(\vec{r})+\lambda\delta(\vec{r [stackexchange, 5 points]

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