Premium
A tensor representation of the real spherical functions for the continuous group O 3 + in cartesian coordinates: Example of eulerian rotations
Author(s) -
Boudeville Yves,
RousseauViolet Jeanne
Publication year - 1990
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560370504
Subject(s) - eulerian path , cartesian coordinate system , cartesian tensor , scalar (mathematics) , frame of reference , reference frame , representation (politics) , group (periodic table) , mathematics , generalized coordinates , cross product , orthogonal coordinates , mathematical analysis , spherical coordinate system , bipolar coordinates , frame (networking) , log polar coordinates , classical mechanics , physics , geometry , computer science , tensor density , tensor field , quantum mechanics , telecommunications , lagrangian , politics , political science , law , exact solutions in general relativity
The aim of this article is to give a practical way for the use of real spherical functions in another frame than the frame in which they have been defined. For instance, we calculate physical properties from a local frame and use them in the general frame, deduced one from the other by Eulerian rotations on the coordinates. The power of the method is in the use of cartesian coordinates and in the definition of a scalar product between these functions to set up the complete vectorial space generated by these representations of the group O 3 + .