Anharmonic oscillator, optimal basis expansion, and the Schwartz's length

Details Anharmonic oscillator, optimal basis expansion, and the Schwartz's length Anharmonic oscillator, optimal basis expansion, and the Schwartz's length

2010-10-21

arxiv.org/abs/1010.4387v3

Physics

Mathematical Physics

15 pages, 4 figure

Scientific paper

We present three optimal lengths for highly accurate calculation of the eigenvalues and the eigenfunctions of the anharmonic oscillator with trigonometric basis functions. We show that the Schwartz's length gives the most accurate results for all values of $k$. This formula, in its original context, imposes a constraint on the mesh spacing $h$ and the cutoff number $N$ which results in exponentially decrease of their overall errors. In this paper, we show that this length can be also addressed in direct diagonalization of the Schr\"odinger equation with the particle in a box basis functions where $Nh$ plays the role of the basis domain $L$.

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