## Fifty years of eigenvalue perturbation theory.(English)Zbl 0739.47006

The author gives an review of eigenvalue perturbation theory starting from famous F. Rellich’s works. It turns out, that many of the examples of interest in quantum physics do not fit into the scheme of regular perturbation theory.
The following models are discussed in detail: isoelectric atoms, autoionizing states, the anharmonic oscillator, double wells, Zeeman and Stark effects and Berry’s phase.
It must be noted that many questions of the regular perturbation theory may be completely solved by the Newton diagram method of branching theory [see M. M. Vainberg and V. A. Trenogin, “The theory of branching of solutions of nonlinear equations” (1974; Zbl 0274.47033)].

### MSC:

 47A55 Perturbation theory of linear operators 47N50 Applications of operator theory in the physical sciences 47A75 Eigenvalue problems for linear operators

Zbl 0274.47033
Full Text:

### References:

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