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Computation of the Semiclassical Limit of the Schrödinger Equation with Phase Shift by a Level Set Method

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In this paper, we show how the level set method, developed in [Cheng, Liu and Osher, (2003). Comm. Math. Sci. 1(3), 593–621; Jin, Liu, Osher and Tsai, (2005). J. comp. Phys. 205, 222–241; Jin and Osher, (2003). Comm. Math. Sci. 1(3), 575–591] for the numerical computation of the semiclassical limit of the Schrödinger equation, can be amended to include the phase shift using the Keller-Maslov index. This gives a more accurate approximation of the physical observables for multivalued solutions in the semiclassical limit. Numerical examples in one and two spaces dimensions demonstrate the improved accuracy of our approach away from caustics.

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, Madison, WI, 53706, USA

    Shi Jin & Xu Yang

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  1. Shi Jin
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  2. Xu Yang
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Correspondence to Xu Yang.

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Jin, S., Yang, X. Computation of the Semiclassical Limit of the Schrödinger Equation with Phase Shift by a Level Set Method. J Sci Comput 35, 144–169 (2008). https://doi.org/10.1007/s10915-007-9137-9

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  • DOI: https://doi.org/10.1007/s10915-007-9137-9

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