Anharmonic oscillator and double-well potential: approximating eigenfunctions
Turbiner, Alexander V
arXiv, 0506033 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-06-13
Classification:  Mathematical Physics,  Condensed Matter - Statistical Mechanics,  High Energy Physics - Theory,  Quantum Physics 
@article{0506033,
     author = {Turbiner, Alexander V},
     title = {Anharmonic oscillator and double-well potential: approximating
  eigenfunctions},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0506033}
}

Turbiner, Alexander V. Anharmonic oscillator and double-well potential: approximating
  eigenfunctions. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0506033/