On power series representing solutions of the one-dimensional time-independent Schrödinger equation
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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.
Keywordstime-independent Schrödinger equation Helmholtz equation exact solution in the form of a power series
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- 6.D. A. Komarov, S. P. Morev, A. N. Darmaev, and A. Yu. Ryadnov, “Numerical solution of the Schrödinger equation for an electron in an arbitrarily shaped potential well,” Radiotekh. Elektron. 59 (8), 799–803 (2014).Google Scholar