In a recent paper [J. Math. Phys. 8, 423 (1967)], Dyson and Lenard gave a lower bound of the N‐particle Hamiltonian, Coulomb interaction, which was quadratic in N. An essential step in their proof is the fact that the one‐particle Hamiltonian with Yukawa potential −r−1e−μr is nonnegative if μ is not less than some value. The aim of this paper is to improve this positivity result and thereby improve the lower bound of Dyson and Lenard.

1.
F. J.
Dyson
 and
A.
Lenard
,
J. Math. Phys.
8
,
423
(
1967
).
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2.
Hans F. Weinberger, “Lower Bounds for Eigenvalues” (unpublished).
3.
John
Piepenbrink
, “
Rellich Densities and an Application to Unconditionally Nonoscillatory Elliptic Equations
,”
Pacific J. Math.
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, No.
3
(
1972
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4.
John Piepenbrink, “The Oscillation Constant for Second Order Elliptic Equations” (unpublished).
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© 1972 The American Institute of Physics.
1972
The American Institute of Physics
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