An inequality is derived which gives an upper bound of the number of bound states in the
l-th partial wave (
l=0, 1, …) of the two-body Schrödinger equation with a spherically symmetric potential function in the
n-dimensional space (
n=1, 2 …). This is a generalization of Bargmann's inequality for the case
n=3. The generalization is straightforward for the case
l{≥}1 with
n=2 and
l{≥}0 with
n{≥}3. 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
l=−½,
n=3, which is equivalent to the case
l=0,
n=2, is reobtained.
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