Linear Canonical Transformations in the Theory of Vibrationalhyphen;Rotational Interactions in Molecules. A Practical Closed FormNhyphen;Dimensional Procedure

摘要

A generalNhyphen;dimensional linear transformation is written, wherein each original variablexi, pilpar;iequals;1, middot;middot;middot;, Nrpar;is expressed in closed form as a linear function of the 2Ntransformed variablesxiprime;,thinsp;piprime;A set of 2N2hyphen;Nrelationships between the linear coefficients is then derived for the transformation to be canonical. This procedure provides one with the most general form ofNhyphen;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.