Accurate energy spectrum for double-well potential: periodic basis

Details Accurate energy spectrum for double-well potential: periodic basis Accurate energy spectrum for double-well potential: periodic basis

2006-11-14

arxiv.org/abs/math-ph/0611033v3

Mol. Phys. 108 (2010) 1949

Physics

Mathematical Physics

15 pages, 5 figures, to appear in Molecular Physics

Scientific paper

We present a variational study of employing the trigonometric basis functions satisfying periodic boundary condition for the accurate calculation of eigenvalues and eigenfunctions of quartic double-well oscillators. Contrary to usual Dirichlet boundary condition, imposing periodic boundary condition on the basis functions results in the existence of an inflection point with vanishing curvature in the graph of the energy versus the domain of the variable. We show that this boundary condition results in a higher accuracy in comparison to Dirichlet boundary condition. This is due to the fact that the periodic basis functions are not necessarily forced to vanish at the boundaries and can properly fit themselves to the exact solutions.

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