High-Precision Numerical Determination of Eigenvalues for a Double-Well Potential Related to the Zinn-Justin Conjecture

Details High-Precision Numerical Determination of Eigenvalues for a Double-Well Potential Related to the Zinn-Justin Conjecture High-Precision Numerical Determination of Eigenvalues for a Double-Well Potential Related to the Zinn-Justin Conjecture

2004-02-16

arxiv.org/abs/quant-ph/0402101v2

J.Phys.A38:6785-6792,2005

Physics

Quantum Physics

Substantial changes including the title and the content of the paper 8 pages, 2 figures, 3 tables

Scientific paper

10.1088/0305-4470/38/30/012

A numerical method of high precision is used to calculate the energy eigenvalues and eigenfunctions for a symmetric double-well potential. The method is based on enclosing the system within two infinite walls with a large but finite separation and developing a power series solution for the Schr$\ddot{o}$dinger equation. The obtained numerical results are compared with those obtained on the basis of the Zinn-Justin conjecture and found to be in an excellent agreement.

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