Journal of Mathematical Physics

Symmetry of the Ground Level of a Hamiltonian

Walter H. Kleiner, T. A. Kaplan

Published Feb 1, 1969• 5 citations

Abstract

A general connection between nodelessness and symmetry of a function is pointed out. It is proved that a real nodeless energy eigenfunction with energy E has a nonzero part which also is an eigenfunction with energy E and which under coordinate transformations has the full symmetry of the Hamiltonian. This result can be applied to many systems of physical interest for which the ground-state energy eigenfunction is known from the nature of the Hamiltonian to be nodeless. Simple counterexamples are given however, to show that not all Hamiltonians have a nodeless ground-state energy eigenfunction.

DOI: 10.1063/1.1664838

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