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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.

Keywords

time-independent Schrödinger equation Helmholtz equation exact solution in the form of a power series 

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.VNIIFTRIMendeleevoRussia

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