Journal
LETTERS IN MATHEMATICAL PHYSICS
Volume 74, Issue 2, Pages 169-180Publisher
SPRINGER
DOI: 10.1007/s11005-005-0012-z
Keywords
Schroedinger equation; anharmonic oscillator; double-well potential; eigenfunctions; approximations
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A simple uniform approximation of the logarithmic derivative of the ground state eigenfunction for both the quantum-mechanical an harmonic oscillator and the double-well potential given by V = m(2)x(2) + gx(4) at arbitrary g >= 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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