On the Nonconservation of the Number of Nodal Cells of Eigenfunctions

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Published under licence by IOP Publishing Ltd
, , Citation M. Caffarel et al 1992 EPL 20 581 DOI 10.1209/0295-5075/20/7/002

0295-5075/20/7/581

Abstract

The theorem stating that the number of nodal cells of a pure eigenfunction of a Hamiltonian with a smooth and uniformly bounded potential may change as the potential is continuously varied, is illustrated by constructing a particular two-dimensional Hamiltonian (two coupled oscillators) of which one of the eigenfunctions exhibits the nonconservation property. The analytical form of both the potential (a six-order polynomial) and the eigenfunction is given.

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10.1209/0295-5075/20/7/002