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Recursive Weak- and Strong Coupling Expansions in a Cosine Potential

Bodo Hamprecht
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Abstract

For the Cos(2x)-Potential the coefficients of the weak- and strong coupling perturbation series of the ground state energy are constructed recursively. They match the well-known expansion coefficients of the Mathieu equation's characteristic values. However presently there is no physically intuitive method to extract the coefficients of the strong coupling series from those of the weak one. The standard rule while giving exellent results for the anharmonic oscillator fails completely in this case.

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Bodo Hamprecht. 2002-11-11. Recursive Weak- and Strong Coupling Expansions in a Cosine Potential. https://arxiv.org/abs/quant-ph/0211057

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