Anharmonic oscillator and double-well potential: approximating eigenfunctions

Details Anharmonic oscillator and double-well potential: approximating eigenfunctions Anharmonic oscillator and double-well potential: approximating eigenfunctions

2005-06-13

arxiv.org/abs/math-ph/0506033v1

Lett.Math.Phys. 74 (2005) 169-180

Physics

Mathematical Physics

14 pages, 3 figures, 2 tables

Scientific paper

10.1007/s11005-005-0012-z

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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