Hybrid orbitals and the runge–lenz vector

✍ Scribed by Lawrence L. Lohr Jr.

• Book ID: 104578880
• Publisher: John Wiley and Sons
• Year: 1976
• Tongue: English
• Weight: 556 KB
• Volume: 10
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560100511

✦ Synopsis

Abstract

Matrix elements of the Runge–Lenz vector A are presented for those linear combinations of degenerate hydrogenic functions often referred to as hybrid orbitals. The uncertainties in the components of A for each type of wave‐function are related to the distribution of classical Kepler orbits corresponding to each function. Matrix elements of A with respect to radially nodeless Slater functions are presented, as these functions are often used as a basis set in atomic and molecular calculations. The properties of A for a piecewise Coulombic central field are discussed in relation to the description of penetrating orbits in the old quantum theory. Simultaneous eigenfunctions of A and the Hamiltonian cannot be chosen for the piecewise Coulombic field because of a discontinuity in the radial derivative of the potential energy.