Einführung in die Wellenmechanik

Abstract

It is shown that if II is the negative energy operator, and @ any function satisfying the boundary conditions of quantum dynamics and possessing the symmetry properties characteristic of a given spectral series, then E = fysH+r is a lower limit to the term-value of the lowest level of that series. If the integral is evaluated for various @'s, the largest value obtained will be the best approximation to this term value. The method is applied to various electronic configurations with satisfactory results. The degree to which @ approximates the wave function of the state is not determined, but it is shown to be likely that the approximation is not good at large distances from the nucleus. 'HE empirical interpretation of x-ray spectra has long been based on the idea that each electron of an inner shell screens the outer electrons from the field of the nucleus. The outer electrons are supposed to move in an approximately central field, much as though the inner electrons were not present and the nucleus had an effective charge less than its true charge. Millikan and Bowen have also shown that this idea is applicable to many optical spectra. Quantum dynamics has furnished a qualitative justification for this idea, but the effective nuclear charges have never been deduced from first principles in any systematic way. It is true that L. Pauling has obtained numerical values for them which are in excellent agreement with observation, but his calculation begins with the wave equation of a single electron moving in the field of an artificial distribution of charges on spherical surfaces. This amounts to assuming the general form of the result, and neglecting some of the finer features of the problem. J. FrenkeP has used the method which forms the subject of the present paper. He calculates the screening constant for the normal state of helium-like atoms, but assumes it to be applicable to any state. It was found empirically (cf. Section 5) that the method fails miserably when applied to (Is)(2s) 2'S, but, remarkably enough, gives very good results for (1s)(2s) 2s5. This is shown to be a consequence of a definite limitation on the method, which is applicable only to the lowest state of any spectral series. (Section 1.). The method is analogous to that first used by Ritz' to calculate characteristic numbers. The Ritz method has already been used to solve problems ' L.