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Large-order perturbation theory for the O(2) anharmonic oscillator with negative anharmonicity and for the double-well potential

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DOI: 10.1016/b978-0-444-88597-5.50032-6

Abstract

Abstract For the O(2) anharmonic oscillator with negative anharmonicity and one-dimensional double-well potential U(x) = (x2−R2)2/8R2, R is a large parameter for both problems, conventional Rayleigh–Schrödinger expansions in power series of 1/R2 for the energy eigenvalues agree. We studied asymptotic expansions for the eigenvalues which contain, in addition to the perturbation series, exponentially small terms in R2 due to the tunnelling through corresponding potential barriers. Numerical calculations are also performed and comparisons with the asymptotic formulae are given.

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