Complex transformation method and resonances in one-body quantum systems. (English) Zbl 0568.47008
The author treats the resonance problem in one-body systems via a new spectral deformation method. A third complex transformation method is given which may be compared to the local distortion technique of Babbitt and Balslev and the exterior complex scaling method of Simon. As with these latter methods the idea is to extend the domain of application of the complex scaling method of Combes and Balslev in the study of resonances. His method generalizes the complex scaling method in a way which is close in spirit to the local distortion technique. It is applicable to the multicenter problems in which each potential can be represented more or less as a sum of exponentially decaying and dilation analytic spherically symmetric parts. In an addendum to his paper the author notes that condition 3.8 has be modified.
Reviewer: M.Thompson
MSC:
| 47A40 | Scattering theory of linear operators |
| 81U10 | \(n\)-body potential quantum scattering theory |
| 35P25 | Scattering theory for PDEs |
Keywords:
resonance problem in one-body systems; spectral deformation method; complex transformation method; local distortion technique; exterior complex scaling method; multicenter problemsReferences:
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