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Anharmonic oscillator and double-well potential: approximating eigenfunctions

Alexander V Turbiner
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Abstract

A simple uniform approximation of the logarithmic derivative of the ground state eigenfunction for both the quantum-mechanical anharmonic oscillator and the double-well potential given by $V= m^2 x^2+g x^4$ at arbitrary $g \geq 0$ for $m^2>0$ and $m^2<0$, respectively, is presented. It is shown that if this approximation is taken as unperturbed problem it leads to an extremely fast convergent perturbation theory.

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Alexander V Turbiner. 2005-06-13. Anharmonic oscillator and double-well potential: approximating eigenfunctions. https://doi.org/10.1007/s11005-005-0012-z

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