Theorie quantique du pouvoir rotatoire magnetique des molecules diamagnetiques. I. Formalisme general

Abstract

AbstractsThe quantum theory of the Faraday effect or magnetic rotatory power is set up for diamagnetic molecules and is based upon a variation-perturbation method which, unlike the usual Dirac perturbation theory, needs only the knowledge of the wave function who) of the ground state of the non-perturbed molecule. The principle of this theory includes in the expression of the perturbed wave function, vectors which characterize the contribution of the different fields of perturbation. The quantities which describe the Faraday effect, obtained from the calculation of the electric and magnetic macroscopic dipole moments, are expressed from yho) and the vectors precedently introduced. They are determined by a variation calculus. La thtorie quantique de l'effet Faraday ou pouvoir rotatoire magnttique est dtveloppte pour les moltcules diamagnttiques en utilisant une mtthode de variation-perturbation qui contrairement a la thCorie des perturbations de Dirac habituellement utiliste, ne ntcessite que la connaissance de la fonction d'onde yho) de l'ttat fondamental de la moltcule non perturbte. Le principe de cette thtorie consiste a faire apparaitre dans l'expression de la fonction d'onde perturbte des vecteurs caracttrisant la contribution des difftrents champs perturbateurs. Les termes responsables de l'effet Faraday, dtduits d'un calcul des moments dipolaires tlectriques et magnttiques macroscopiques, sont exprimts en fonction de yAo) et des divers vecteurs introduits. Ceux-ci sont dttermints par un calcul variationnel.Die Quantentheorie des Faradayeffekts wurde fur diamagnetische Molekiile diskutiert. Die benutzte Variations-Storungsmethode braucht nur die Wellenfunktion yho) des Grundzustands des ungestorten Molekiils. In dem Ausdruck fur die gestorte Wellenfunktion erscheinen gewisse Vektoren, die die Beitrage der verschiedenen storenden Felder characterisieren. Diese Vektoren wurden mit einer Variationsrechnung bestimmt. Die Glieder, die fur den Faradayeffekt verantwortlich sind, wurden in yho) und den verschiedenen Vektoren ausgedruckt.

Definition of invariant molecular tensors in an origin change. III. Comparison of the methods suitable for the obtainment of invariant tensors for refraction and the Faraday effect

“…-The present study is mainly a comparison of procedures using the variationperturbation method. The results obtained would be identical in the case of a perturbation method, since the link between both methods is easily established [6]. The main interest of this comparison is to suggest how we should proceed, from a method where the electric and magnetic multipoles are separated (type-S method) to obtain, even so, invariant tensors.…”

“…(a) Using a type SEPV method, Smet [6] has obtained an expression for Verdet's constant, formally similar to formula (31) of Paper 11; that is, with coefficients we note qSm and f m ( Paper 111, and therefore ensure its invariance. We explain briefly how to proceed, passing from the coefficient lSm to the invariant coefficient l.…”

Definition of invariant molecular tensors in an origin change. I. General formalism

“…In a further paper, this method will be applied to Faraday effect whose previous study [3] has put aside some problems raised by invariance in a micro-origin change.…”

Definition of invariant molecular tensors in an origin change. II. Refraction and Faraday effect

“…The expansion of f" has been given previously [3]. When keeping only the terms useful for a further calculation, the expansion of function f:$B is given by where the new unknown function fz$@"'-) are the solutions of equations easy to obtain from [I(7b)].…”

“…To obtain terms of this form from (19), we must expand the exponentials and the functions f to the power 2 of vector kl and power 1 of vector kz. The expansion of f" has been given previously [3]. When keeping only the terms useful for a further calculation, the expansion of function f:$B is given by where the new unknown function fz$@"'-) are the solutions of equations easy to obtain from [I(7b)].…”