Canonically Transformed Detectors Applied to the Classical Inverse Scattering Problem

Details Canonically Transformed Detectors Applied to the Classical Inverse Scattering Problem Canonically Transformed Detectors Applied to the Classical Inverse Scattering Problem

2005-04-08

arxiv.org/abs/physics/0504053v1

Journal of Nonlinear Mathematical Physics, 12, Supplement 1, 404 (2005)

Physics

Classical Physics

8 pages, 15 figures. Better figures can be found in the original article, wich can be found in http://www.sm.luth.se/~norber

Scientific paper

10.2991/jnmp.2005.12.s1.33

The concept of measurement in classical scattering is interpreted as an overlap of a particle packet with some area in phase space that describes the detector. Considering that usually we record the passage of particles at some point in space, a common detector is described e.g. for one-dimensional systems as a narrow strip in phase space. We generalize this concept allowing this strip to be transformed by some, possibly non-linear, canonical transformation, introducing thus a canonically transformed detector. We show such detectors to be useful in the context of the inverse scattering problem in situations where recently discovered scattering echoes could not be seen without their help. More relevant applications in quantum systems are suggested.

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