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Piecewise constant potentials and discrete ambiguities

Abstract : This work is devoted to the study of discrete ambiguities. For parametrized potentials, they arise when the parameters are fitted to a finite number of phase-shifts, which generate phase-equivalent potentials. Such equivalence was suggested to be due to the modulo π uncertainty inherent to phase determinations. We show that a different class of phase-equivalent potentials exists. To this aim, use is made of piecewise-constant potentials, intervals of which are defined by the zeros of their regular solutions of the Schrödinger equation. We give a classification of the ambiguities in terms of indices which include the difference between exact phase modulo π and the numbering of the wave function zeros.
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http://hal.in2p3.fr/in2p3-00533677
Contributor : Sophie Heurteau <>
Submitted on : Monday, November 8, 2010 - 10:34:33 AM
Last modification on : Wednesday, September 16, 2020 - 4:08:13 PM

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M. Lassaut, R.J. Lombard. Piecewise constant potentials and discrete ambiguities. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2010, 43, pp.445210. ⟨10.1088/1751-8113/43/44/445210⟩. ⟨in2p3-00533677⟩

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