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  • American Institute of Physics (AIP)  (2)
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  • 1
    Electronic Resource
    Electronic Resource
    High- and low-energy estimates for the Dirac equation (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 991-1015 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The scattering theory for the Dirac equation with radial potential is studied. The leading term at high energy is computed and Parzen's theorem is proved. In the case of zero mass, the behavior at low energy is analyzed, which turns out to be different from the low-energy behavior for positive mass, and an appropriate version of Levinson's theorem is proved under the assumption that the potential is integrable over (0,∞). © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531138
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  • 2
    Electronic Resource
    Electronic Resource
    The geometrical approach to multidimensional inverse scattering (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 3902-3921 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We prove that in multidimensional short-range potential scattering the high velocity limit of the scattering operator of an N-body system determines uniquely the potential. For a given long-range potential the short-range potential of the N-body system is uniquely determined by the high velocity limit of the modified Dollard scattering operator. Moreover, we prove that any one of the Dollard scattering operators determines uniquely the total potential. We obtain as well a reconstruction formula with an error term. Our simple proof uses a geometrical time-dependent method. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530937
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