Abstract
This paragraph is devoted to the application of the FM developed in §.44 to a widely studied power series with zero convergence radius: the RSPT for anharmonic oscillators. As discussed before, the anharmonic oscillator models are closely related with a λϕ2M field theory (Appendix B). The model is also found when describing molecular vibrations, diffusion processes, laser theories, etc. (Appendix A). We have resorted to this model time and again in preceding chapters but right now we are able to obtain highly accurate results.
“I had stated,... solutions of physical problems must always be in finite terms or convergent series, otherwise nonsense is made...Then came a partial renoval of ignorant blindness. In some physical problems divergent series are actually used.”
O. Heaviside, Electromagnetic Theory,1889.
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Arteca, G.A., Fernández, F.M., Castro, E.A. (1990). Application of the FM to the Anharmonic Oscillator. In: Large Order Perturbation Theory and Summation Methods in Quantum Mechanics. Lecture Notes in Chemistry, vol 53. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93469-8_17
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