A new proof for the convergent iterative solution of the degenerate quantum double-well potential and its generalization |
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Authors: | R Friedberg TD Lee |
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Institution: | a Physics Department, MC 5208, Columbia University, 538 West 120th Street, New York, NY 10027, USA b China Center of Advanced Science and Technology (CCAST) (World Laboratory), P.O. Box 8730, Beijing 100080, PR China c RIKEN BNL Research Center (RBRC), Brookhaven National Laboratory, Upton, NY 11973, USA |
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Abstract: | We present a new and simpler proof for the convergent iterative solution of the one-dimensional degenerate double-well potential. This new proof depends on a general theorem, called the hierarchy theorem, that shows the successive stages in the iteration to form a monotonically increasing sequence of approximations to the energy and to the wavefunction at any point x. This important property makes possible a much simpler proof of convergence than the one given before in the literature. The hierarchy theorem proven in this paper is applicable to a much wider class of potentials which includes the quartic potential. |
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