| Issue |
EPL
Volume 126, Number 3, May 2019
|
|
|---|---|---|
| Article Number | 30003 | |
| Number of page(s) | 7 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/126/30003 | |
| Published online | 19 June 2019 | |
On the Heisenberg condition in the presence of redundant poles of the S-matrix
1 Wave-scattering.com
2 School of Engineering and Information Technology, University of New South Wales Canberra Northcott Drive, Campbell, ACT 2600, Australia
Received: 4 April 2019
Accepted: 14 May 2019
For the same potential as originally studied by Ma (Phys. Rev., 71 (1947) 195) we obtain analytic expressions for the Jost functions and the residue of the S-matrix of both i) redundant poles and ii) the poles corresponding to true bound states. This enables us to demonstrate that the Heisenberg condition is valid in spite of the presence of redundant poles and a singular behaviour of the S-matrix for 
. In addition, we analytically determine the overall contribution of redundant poles to the asymptotic completeness relation, provided that the residue theorem can be applied. The origin of redundant poles and zeros is shown to be related to peculiarities of analytic continuation of a parameter of two linearly independent analytic functions.
PACS: 03.65.Nk – Scattering theory / 03.65.Ge – Solutions of wave equations: bound states / 03.65.-w – Quantum mechanics
© EPLA, 2019
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