Linear Canonical Transformations in the Theory of Vibrational-Rotational Interactions in Molecules. A Practical Closed Form N-Dimensional Procedure

Abstract

A general N-dimensional linear transformation is written, wherein each original variable xi, pi (i=1, ···, N) is expressed in closed form as a linear function of the 2N transformed variables xi′, pi′ A set of 2N2-N relationships between the linear coefficients is then derived for the transformation to be canonical. This procedure provides one with the most general form of N-dimensional linear canonical quantum mechanical transformation, while giving the operators in closed form. The procedure is compared with the alternate method of using unitary generators, and its advantages over that method are discussed.