Anharmonic oscillator and the optimized basis expansion
Mathematical Physics
2012-12-07 v5 math.MP
Quantum Physics
Abstract
We introduce various optimization schemes for highly accurate calculation of the eigenvalues and the eigenfunctions of the one-dimensional anharmonic oscillators. We present several methods of analytically fixing the nonlinear variational parameter specified by the domain of the trigonometric basis functions. We show that the optimized parameter enables us to determine the energy spectrum to an arbitrary accuracy. Also, using the harmonic oscillator basis functions, we indicate that the resulting optimal frequency agrees with the one obtained by the principle of the minimal sensitivity.
Cite
@article{arxiv.1010.4387,
title = {Anharmonic oscillator and the optimized basis expansion},
author = {Pouria Pedram},
journal= {arXiv preprint arXiv:1010.4387},
year = {2012}
}
Comments
15 pages, 7 figures, to appear in Applied Mathematics and Computation