×

Separation of variables in systems of partial differential equations which are invariant with respect to the group O(3). (Russian. English summary) Zbl 0564.35082

Algebraic-theoretical methods in the problems of mathematical physics, Collect. sci. Works, Kiev 1983, 87-98 (1983).
[For the entire collection see Zbl 0529.00024.]
The author obtains some results having application to the separation of variables in systems of partial differential equations which are invariant with respect to the group O(3). The explicit form of the operator \(\vec S\cdot \vec x\) in with respect to a spherical spinors basis is found, where \(\vec x\) is a three-vector of independent variables, \(\vec S\) is an arbitrary matrix which transforms as a vector under special rotations. These results allow to obtain the equation for the radial wave function of an arbitrary spin particle which is described by the Galerkin-Yaglom equation.
Reviewer: H.Kilp

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35A30 Geometric theory, characteristics, transformations in context of PDEs

Citations:

Zbl 0529.00024