Exact solutions for spherically confined hydrogen-like atoms

B. L. Burrows*, M. Cohen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

Abstract

We present exact analytical solutions for the much-studied problem of a hydrogen-like atom confined in a spherical box of radius R. These solutions, which are obtained for all states and all R, are expressed directly in terms of the Kummer M-functions whose analytical and numerical properties are well known, and may be calculated using standard computing packages. The solutions are illustrated by precise calculations that yield accurate energies E for any given radius R, or for R when E is known. In the special case where E = 0, it is shown that the solution may be expressed in terms of Bessel functions. Finally, the physical assumptions made in applying this model to describe atomic confinement are discussed critically.

Original languageEnglish
Pages (from-to)478-484
Number of pages7
JournalInternational Journal of Quantum Chemistry
Volume106
Issue number2
DOIs
StatePublished - Feb 2006

Keywords

  • Algebraic
  • Confined hydrogen
  • Exact solutions
  • Kummer M functions
  • Stationary states

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