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 language | English |
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Pages (from-to) | 478-484 |
Number of pages | 7 |
Journal | International Journal of Quantum Chemistry |
Volume | 106 |
Issue number | 2 |
DOIs | |
State | Published - Feb 2006 |
Keywords
- Algebraic
- Confined hydrogen
- Exact solutions
- Kummer M functions
- Stationary states