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Perturbation theory without power series: iterative construction of non-analytic operator spectra
by Matteo Smerlak
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Submission summary
| Authors (as registered SciPost users): | Matteo Smerlak |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2105.04972v4 (pdf) |
| Date submitted: | Jan. 2, 2022, 1:57 p.m. |
| Submitted by: | Matteo Smerlak |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
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| Approach: | Theoretical |
Abstract
It is well known that quantum-mechanical perturbation theory often gives rise to divergent series that require proper resummation. Here I discuss simple ways in which these divergences can be avoided in the first place. Using the elementary technique of relaxed fixed-point iteration, I obtain convergent expressions for various challenging ground states wavefunctions, including quartic, sextic, and octic anharmonic oscillators, the hydrogenic Zeeman problem, and the Herbst-Simon Hamiltonian (with finite energy but vanishing Rayleigh-Schrödinger coefficients), all at arbitrarily strong coupling. These results challenge the notion that non-analytic functions of coupling constants are intrinsically "non-perturbative". A possible application to exact diagonalization is briefly discussed.