The Quantum Mechanical Hamiltonian of Rotating-Vibrating Polyatomic Molecules and an Exact Solution
Estes, Donald William
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https://hdl.handle.net/2142/70195
Description
Title
The Quantum Mechanical Hamiltonian of Rotating-Vibrating Polyatomic Molecules and an Exact Solution
Author(s)
Estes, Donald William
Issue Date
1982
Department of Study
Chemistry
Discipline
Chemistry
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Chemistry, Physical
Abstract
An exact quantum mechanical vibration-rotation Hamiltonian for an arbitrary polyatomic molecule is obtained using well-established techniques of differential geometry. The difficulties and the ambiguities in the traditional approach to this problem--that of quantization--are then investigated. In this unified treatment of linear and nonlinear molecules, the reasons that previously have led to the exclusion of linear systems from an otherwise general approach are discussed and are shown to be fallacious. In particular, the widely accepted proof of the singularity of the effective moment of inertia tensor of the classical Hamiltonian of Wilson and Howard is shown to be incorrect.
The classical limit of the quantum mechanical vibration-rotation Hamiltonian is obtained and a method for identifying angular momentum operators from their classical counterparts is presented. In lieu of this identification, a quantum mechanical treatment of angular momentum in a rotating frame is developed. In this treatment, the well-known anomalies of these angular momentum operators are shown to be misleading.
A new method for an exact solution of the corresponding Schrodinger equation of nuclear motion on a bound-state potential surface is then developed. The approach is independent of the amplitude of molecular vibration. The coupling terms which give rise to Fermi resonance, Coriolis interaction, and l-type doubling are retained exactly. In presenting the results for the carbon dioxide molecule, questions as to the validity of its standard spectroscopic identification are raised.
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