1010.4387 (Pouria Pedram)

Anharmonic oscillator and the optimized basis expansion    [PDF]

Pouria Pedram

We discuss the optimization of nonlinear parameters in the Rayleigh-Ritz variational scheme on the example of bound state determination for one-dimensional anharmonic oscillators. Using the trigonometric basis set, we present and compare several methods of analytically fixing the parameter represented by the width of the finite domain. 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. We show that the optimized parameter enables us to determine the energy spectrum to an arbitrary accuracy.

View original: http://arxiv.org/abs/1010.4387