Hybrid orbitals and the Runge--Lenz vector. [Matrix elements]

Journal Article · Wed Sep 01 04:00:00 EDT 1976 · Int. J. Quant. Chem.; (United States)

DOI:https://doi.org/10.1002/qua.560100511· OSTI ID:7327909

Lohr, Jr, L L

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.

• Research Organization: Univ. of Michigan, Ann Arbor
• OSTI ID: 7327909
• Journal Information: Int. J. Quant. Chem.; (United States), Journal Name: Int. J. Quant. Chem.; (United States) Vol. 10:5; ISSN IJQCB
• Country of Publication: United States
• Language: English

Related Subjects

640302* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
COULOMB FIELD
CRYOGENIC FLUIDS
DISTRIBUTION
EIGENFUNCTIONS
ELECTRIC FIELDS
ELECTRONIC STRUCTURE
ELEMENTS
ENERGY
FLUIDS
FUNCTIONS
HAMILTONIANS
HYDROGEN
MATHEMATICAL OPERATORS
MATRIX ELEMENTS
NONMETALS
POTENTIAL ENERGY
QUANTUM OPERATORS
SLATER METHOD
TENSORS
VECTORS
WAVE FUNCTIONS