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  Home > JCE Print > Journal of Chemical Education > Issues > 1997  > August  >
Research: Science and Education
Variational Treatment of Attractive Central Power-Law Potentials
B. Cameron Reed
Department of Physics, Alma College, 614 West Superior St., Alma, MI 48801-1599
Cover
August 1997
Vol. 74 No. 8
p. 935
Abstract
Utilizing the normalized hydrogenic ground-state wavefunction as a trial solution, this paper addresses application of the variational principle to three-dimensional attractive central potentials of the form V(r) = -k/rn (k, n > 0; 0 < r < ). While the calculations lead to a constraint that restricts consideration to 0 < n < 2, an apparently new conclusion emerges: that, for a given value of the product kµ where µ is the ratio of the mass of the particle trapped in the potential to the mass of the electron, µ = (m/me), there exists a value of n such that the ground-state energy is a maximum, that is, the ground-state is minimally bound. Study of the limiting case shows that there is a critical value of kµ below which this minimal binding does not arise.
More Information
*  Citation
 Reed, B. Cameron. J. Chem. Educ. 1997 74 935.
*  Keywords
 Physical Chemistry, Computational Chemistry, Quantum Chemistry, Theoretical Chemistry
*  History
 Created:
Last Updated:		 July 28, 1999
June 23, 2005
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