A comparison theorem for differential inequalities with applications in quantum mechanics
- 1 February 1980
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 13 (2) , 417-424
- https://doi.org/10.1088/0305-4470/13/2/009
Abstract
A theorem on differential inequalities is proved. By means of this theorem the following result is established. Let psi (r1,r2,r12) denote the ground-state wavefunction of a two-electron atom; then psi (r1,r2r12)1,r1,r'12) for r'1212. Furthermore, a different proof is given, for the hydrogenic molecular ion, of a recent result of Lieb and Simon (1978) on the monotonicity of the electronic part of the Born-Oppenheimer energy with respect to the internuclear distance.Keywords
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