Zum quantenmechanischen Vierkörperproblem

Abstract

In a way similar to that of a former paper, the Schrödinger equation of the four-body problem has been transformed to appropriate coordinates. Besides those of the center of mass, these are the six distances between the four particles and the Eulerian angles describing the orientation of the instantaneous ellipsoid of inertia. By introduction of the angular momentum operatorsL _x″ ,L _y″ ,L _z″ the wave equation — in contrast to the more special three-body problem where the configuration needs must be plane — becomes fully symmetrical not only in the distances but also in these three operators. The solution can again be written as a linear combination of the eigenfunctionsD ^L _MK of the rigid rotator with coefficients depending upon the particle distances. The system of differential equations for these coefficient functions has been given; its behaviour under parity transformation turns out to be rather more involved than in the three-particle case.