IN THE USE OF CONTACT TRANSFORMATIONS IN CLOSED FORM IN THE THEORY OF VIBRATIONAL-ROTATIOANAL INTERACTIONS IN MOLECULES
Creators:Gora, Edwin K.
MetadataShow full item record
Publisher:Ohio State University
Contact transformations have been widely used to transform complicated expressions for Hamiltonians into simplified expressions better suited for various purposes. In the theory of particles interacting with fields a combination of contact transformations in closed form with the so called Van Vleck expansion has been found effective while in the theory of v-r interactions in molecules only expansion procedures have been used. Closed formulas are, however, available for some of the transformations needed in the theory of v-r interactions. The number of such formulas is substantially increased if one defines a new type of special functions. The transformation functions generating these functions are quadratic forms in the canonical variables containing, for two-to four-dimensional problems, two to 12 undetermined parameters while the corresponding special functions depend only upon one to three expansion parameters representing algebraic invariants of the quadratic forms. The transformations thus obtained can be interpreted as generalized rotations either in ordinary or in phase-space. An extension of the formalism to more-dimensional problems is feasible. The mathematical aspects of the formalism are related to Lie group theory.
Author Institution: Physics Department, Providence College Providence
Items in Knowledge Bank are protected by copyright, with all rights reserved, unless otherwise indicated.