Bargmann's Inequalities In Spaces of Arbitrary Dimension

  • Noriaki Seto

    Kyoto University, Japan

Abstract

An inequality is derived which gives an upper bound of the number of bound states in the th partial wave () of the two-body Schrödinger equation with a spherically symmetric potential function in the -dimensional space (). This is a generalization of Bargmann’s inequality for the case . The generalization is straightforward for the case with  and with . After a mathematically rigorous justification of his heuristic argument, Schwinger’s method in his simple proof of Bargmann’s inequality is employed here. Newton’s result for the case ,  , which is equivalent to the case , , is reobtained.

Cite this article

Noriaki Seto, Bargmann's Inequalities In Spaces of Arbitrary Dimension. Publ. Res. Inst. Math. Sci. 9 (1973), no. 2, pp. 429–461

DOI 10.2977/PRIMS/1195192566