Some Remarkable Examples in Eigenvalue Perturbation Theory
نویسندگان
چکیده
We discuss the ground state energy, E(g), of some anharmonic oscillators p2 + x 2 _ 1 + P(x, g), where P(x, g) is a polynomial in x and g. Included is an example with a convergent perturbation series converging to the wrong answer and counterexamples to Dyson's argument on instability implying the divergence of perturbation theory and to the assertion that terms lower order in x to the same order in g do not effect the asymptotics of the perturbation coefficients a n as n ~ oo.
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