The Quantum Mechanical Hamiltonian of Rotating-Vibrating Polyatomic Molecules and an Exact Solution

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Chemistry

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Estes, Donald William

• Chemistry, Physical

Identifier

(UMI)AAI8302855

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/70195