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On power series representing solutions of the one-dimensional time-independent Schrödinger equation

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Abstract

For the equation χ″(x) = u(x)χ(x) with infinitely smooth u(x), the general solution χ(x) is found in the form of a power series. The coefficients of the series are expressed via all derivatives u (m)(y) of the function u(x) at a fixed point y. Examples of solutions for particular functions u(x) are considered.

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Authors and Affiliations

  1. VNIIFTRI, Mendeleevo, Moscow oblast, 141570, Russia

    N. P. Trotsenko

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  1. N. P. Trotsenko
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Correspondence to N. P. Trotsenko.

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Original Russian Text © N.P. Trotsenko, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 6, pp. 973–984.

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Trotsenko, N.P. On power series representing solutions of the one-dimensional time-independent Schrödinger equation. Comput. Math. and Math. Phys. 57, 967–977 (2017). https://doi.org/10.1134/S0965542517060148

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  • DOI: https://doi.org/10.1134/S0965542517060148

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