Geodesic
On power series representing solutions of the one-dimensional time-independent Schrödinger equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 6, pp. 973-984

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For the equation $\chi''(x)=u(x)\chi(x)$ with infinitely smooth $u(x)$, the general solution $\chi(x)$ 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. 
@article{ZVMMF_2017_57_6_a5,
     author = {N. P. Trotsenko},
     title = {On power series representing solutions of the one-dimensional time-independent {Schr\"odinger} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {973--984},
     publisher = {mathdoc},
     volume = {57},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_6_a5/}
}
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N. P. Trotsenko. On power series representing solutions of the one-dimensional time-independent Schrödinger equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 6, pp. 973-984. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_6_a5/