Physics – Mathematical Physics
Scientific paper
1997-02-15
Int.J.Mod.Phys. A12 (1997) 5687-5709
Physics
Mathematical Physics
26 pages including tables, Latex
Scientific paper
10.1142/S0217751X9700298X
We apply a recently proposed approximation method to the evaluation of non-Gaussian integral and anharmonic oscillator. The method makes use of the truncated perturbation series by recasting it via the modified Laplace integral representation. The modification of the Laplace transformation is such that the upper limit of integration is cut off and an extra term is added for the compensation. For the non-Gaussian integral, we find that the perturbation series can give accurate result and the obtained approximation converges to the exact result in the $N \to \infty$ limit ($N$ denotes the order of perturbation expansion). In the case of anharmonic oscillator, we show that several order result yields good approximation of the ground state energy over the entire parameter space. The large order aspect is also investigated for the anharmonic oscillator.
Mizutani Naoki
Yamada Hirofumi
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