Variational Treatment of Attractive Central Power-Law Potentials

B. Cameron Reed
Department of Physics, Alma College, 614 West Superior St., Alma, MI 48801-1599
J. Chem. Educ., 1997, 74 (8), p 935
DOI: 10.1021/ed074p935
Publication Date (Web): August 1, 1997
History, Education, and Documentation

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.

Keywords (Audience):

Upper-Division Undergraduate

Keywords (Domain):

Physical Chemistry

Keywords (Subject):

Computational Chemistry
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  • Received: August 03, 2009

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