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Calculating probabilities without quadrature

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Abstract

It is shown that a direct method for bound states can give the integrated probability over a given region and also the normalised squared wavefunction at a given point without using any quadratures or wavefunction storage. The method is tested on a known example and is then applied to an asymmetric double well potential and also to find the probability of penetration of a particle into the non-classical region for a single well potential.

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Authors and Affiliations

  1. Institut UTINAM (CNRS UMR 6213), 41bis Avenue de l’Observatoire, BP 1615, Besancon Cedex, 25010, France

    J. P. Killingbeck & A. Lakhlifi

  2. Centre for Mathematics, Loten Building, University of Hull, Hull, HU6 7RX, UK

    J. P. Killingbeck

Authors
  1. J. P. Killingbeck
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  2. A. Lakhlifi
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Correspondence to J. P. Killingbeck.

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Killingbeck, J.P., Lakhlifi, A. Calculating probabilities without quadrature. J Math Chem 50, 2051–2060 (2012). https://doi.org/10.1007/s10910-012-0020-z

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  • DOI: https://doi.org/10.1007/s10910-012-0020-z

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