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Exact solutions for spherically confined hydrogen‐like atoms
Author(s) -
Burrows B. L.,
Cohen M.
Publication year - 2005
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.20736
Subject(s) - bessel function , radius , hydrogen atom , exact solutions in general relativity , atom (system on chip) , physics , hydrogen , special functions , quantum mechanics , yield (engineering) , quantum , mathematical physics , mathematics , mathematical analysis , thermodynamics , group (periodic table) , computer science , computer security , embedded system
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. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006
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