Coulomb Interaction in H<sub>2</sub> Molecule for States beyond the Ground State
- 1 The Pennsylvania State University, University College, York, PA, USA
Abstract
The focus of our investigation is to evaluate one of the four contributing terms to the coulombic potential energy of an H 2 molecule. Specifically, we are interested in the term describing the electronic interaction of the charge distribution of one of the hydrogen atoms with the proton of the second atom. Quantum mechanics provides the charge distribution; hence, the evaluation of this term is a semi-classic quantum physics issue. For states other than the ground state the charge distributions are not spherically symmetric; they are functions of the radial and the angular coordinates. For the excited states we develop exact analytic expressions conducive to the potential energies. Because of the functional complexities of the wave functions, the evaluation of the core integrals is carried out utilizing symbolic capabilities of Mathematica [1]. Plots of these energies vs. the distance between the two protons reveal global features.
- A Symbolic Mathematical Computation Program, V10.3, 2015.
- Pauling, L. and Wilson, E.B. (1963) Introduction to Quantum Mechanics with Applications to Chemistry. Dover Publications, Inc., New York.
- Kauzmann, W. (1957) Quantum Chemistry, an Introduction. Academic Press Inc., New York.
- McGlynn, S.P., Vanquickenborne, L.G., Kinoshita, M. and Carroll, D.G. (1972) Introduction to Applied Quantum Chemistry. Holt, Rienart and Winston, Inc., New York.
- Jackson, J.D. (1999) Classical Electromagnetic. 3rd Edition, John Wiley, New York.
- Arfkin, G. (1968) Mathematical Methods for Physicists. Academic Press, New York.
- Davydov, A.S. (1966) Quantum Mechanics. NEO Press, Ann Arbor, Michigan.
- Powell, J.L. and Crasemann, B. (1965) Quantum Mechanics. Addison-Wesley Company, Inc., Boston.
- Schiff, L. (1968) Quantum Mechanics. 3rd Edition, McGraw-Hill Book Company, Tokyo.
- Wallace, P.R. (1984) Mathematical Analysis of Physics Problems. Dover Publications, Inc., New York.
- Beth, H.A. and Salpeter, E.E. (1977) Quantum Mechanics of One- and Two-Electron Atoms. Dover Publications, Inc., New York.
- Flugge, S. (1974) Practical Quantum Mechanics. Springer-Verlag, New York.
- Wolfram Language and System Documentation Center. http://reference.wolfram.com/language/ref/LaguerreL.html