We have found an analytical solution of the 3D stationary Schrödinger equation for any arbitrary potential. The solution has been obtained by transforming the Schrödinger equation to the generalized Ricatti equation, and it has the form of Huygens’ principle for matter waves. We have shown that the solution is more accurate than the JWKB approximation. We discuss possible applications of the solution to molecular dynamics and dynamics of charges in nanostructures.
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Eleuch et al. (2010) studied this question.
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