Reference potential approach to the energy eigenvalue problem of a rotating diatomic molecule

2008 ◽  
Vol 462 (4-6) ◽  
pp. 337-343 ◽  
Author(s):  
Matti Selg ◽  
Vladislav Belous
Keyword(s):  
Eigenvalue Problem ◽  
Diatomic Molecule ◽  
Energy Eigenvalue ◽  
Potential Approach ◽  
Reference Potential

Exact formula for the dipole moment of a one-electron diatomic molecule

1985 ◽  
Vol 401 (1821) ◽  
pp. 373-392 ◽  
Keyword(s):  
Dipole Moment ◽  
Electronic State ◽  
Diatomic Molecule ◽  
Recursion Relation ◽  
Energy Eigenvalue ◽  
Exact Formula ◽  
Electronic Energy ◽  
Moment Function ◽  
Expectation Values ◽  
Feynman Theorem

It is shown that the dipole moment function, μ ( R , Z a , Z b ), for an arbitrary bound electronic state of a one-electron diatomic molecule, with inter-nuclear distance R and atomic numbers Z a , Z b may be expressed exactly in terms of the separation eigenconstant C and the electronic energy eigenvalue W of the Schrödinger equation by means of the Hellmann-Feynman theorem and a new recursion relation. The formula is used to investigate the behaviour of μ in the vicinity of the united atom and when the nuclei are far apart. The generalization required to extend the relation to other expectation values is derived in an appendix.

Liouville Energy Eigenvalue Problem

1971 ◽  
Vol 4 (5) ◽  
pp. 2110-2110
Author(s):  
Hsiao S. Kiang
Keyword(s):  
Eigenvalue Problem ◽  
Energy Eigenvalue

A new treatment of the vibration-Rotation eigenvalue problem for a diatomic molecule

1983 ◽  
Vol 4 (2) ◽  
pp. 218-225 ◽  
Author(s):  
Hafez Kobeissi ◽  
Mounzer Dagher ◽  
Mahmoud Korek ◽  
Ahmad Chaalan
Keyword(s):  
Eigenvalue Problem ◽  
Diatomic Molecule ◽  
Vibration Rotation ◽  
New Treatment

A Class of Exactly Solvable Schrödinger Equations

2005 ◽  
Vol 70 (7) ◽  
pp. 864-880 ◽  
Author(s):  
Jacek Karwowski ◽  
Lech Cyrnek
Keyword(s):  
Eigenvalue Problem ◽  
Exact Solutions ◽  
Diatomic Molecule ◽  
Algebraic Approach ◽  
Schrodinger Equations ◽  
Nuclear Motion ◽  
Schrödinger Equations ◽  
Interacting Particles ◽  
Exactly Solvable

An algebraic approach to solving a class of one-particle Schrödinger equations is presented. As an example, quasi-exact solutions of the eigenvalue problem of a Hamiltonian describing two interacting particles confined in a parabolic well are obtained. This example constitutes a unification and a generalization of several models known in the literature, as the ones of Taut (Phys. Rev. A 1993, 48, 3561) and of Samanta and Ghosh (Phys. Rev. A 1990, 42, 1178). Two confined particles interacting by Coulomb forces and the nuclear motion of a diatomic molecule are discussed as practical implementations.

Liouville Energy Eigenvalue Problem

1970 ◽  
Vol 2 (3) ◽  
pp. 806-810 ◽  
Author(s):  
Hsiao S. Kiang
Keyword(s):  
Eigenvalue Problem ◽  
Energy Eigenvalue
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