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Article: Matrix elements for the morse and coulomb interactions.
- Article from:
- Scientia Magna
- Article date:
- June 1, 2007
- Author:
CopyrightCOPYRIGHT 2007 American Research Press. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Abstract We show the usefulness of the hypervirial theorem to obtain the matrix elements (m|[e.sup.-[gamma]au]|n> for the Morse potential. Besides, it is known that the hydrogenlike atom can be studied as a Morse oscillator, then here we prove that these fact leads to an interesting method to calculate
for the Coulomb interaction.
Keywords Hypervirial theorem, coulomb and Morse potentials, langer transformation, matrix elements.
[section] 1. Introduction
In [1] it was applied the hypervirial theorem (HT) to determine matrix elements for the one-dimensional harmonic oscillator, here we shall employ the HT to obtain (m|[e.sup.-[gamma]au]|n> for ...
<[N.sub.2]|[e.sup.-[gamma]u]|[N.sub.1]><[r.sup.[??]]*>