Abstract
For the Hamiltonianℋ=−∂ 2x -αδ(x)+λx 2 the bound-(λ>0) and resonance(λ<0) states are discussed. The perturbation expansion of the ground-stateɛ 0(λ) in powers ofλ is divergent for allλ. The nature of the singularity atλ=0 is investigated and it turns out, that the perturbation series is asymptotic and therefore useful even forλ<0.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
We thank P. H. Dederichs for helpful discussions.
Rights and permissions
About this article
Cite this article
Dettmann, K., Leibfried, G. A simple example of a singular perturbation expansion. Z. Physik 234, 181–184 (1970). https://doi.org/10.1007/BF01396780
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01396780