Issue |
EPL
Volume 140, Number 3, November 2022
|
|
---|---|---|
Article Number | 32001 | |
Number of page(s) | 6 | |
Section | Mathematical and interdisciplinary physics | |
DOI | https://doi.org/10.1209/0295-5075/ac9e72 | |
Published online | 21 November 2022 |
Perturbation theory without power series: Iterative construction of non-analytic operator spectra
Max Planck Institute for Mathematics in the Sciences - Leipzig, Germany
(a) E-mail: smerlak@mis.mpg.de (corresponding author)
Received: 13 October 2022
Accepted: 28 October 2022
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 wave functions, 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 arbitarily 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.
© 2022 The author(s)
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