Modification of the Delves Variation Principle

have been given previously by B iedenharn and B latt l , and by D elves 2. The variation principle of B iedenharn and Blatt requires trial functions for a complete set of eigenfunctions and is therefore of a rather complicated nature. D elves succeeded in reducing the number of trial functions to two, yjQT(f*) and ipm (r), but his principle determines only the square of the wave function. Moreover, since his variation functional [y0* y 0] is not positiv definite, difficulties may arise in practice as soon as [t/’o* Vo! turnes out to be negativ for certain values of I*. It is the purpose of this paper to show how these difficulties can be removed by a proper modification of the D elves principle. A principle for yi0 itself instead of | ip0 \2 is given showing a close similarity with the original principle. This similarity, however, becomes less dominant, if the new principle is gener­ alized to a wider class of physical quantities. For then it turns out that the principle — unlike the D el­ ves case — permits the calculation of probability am­ plitudes rather than of mean values (sect. 5). As in the paper of D elves the considerations hold for an arbitrary number of dimensions in the configuration space, with f* comprising all variables in the wave function.