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    On the Levinson theorem for Dirac operators

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    Downloads: 291
    Date
    1990-01
    Author
    Klaus, M.
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    Abstract
    For the Dirac equation with potential V(r) obeying ∫∞ 0(1+r)‖V(r)‖d r<∞ we prove a relativistic version of Levinson’s theorem that relates the number of bound states in the spectral gap [−m,m] to the variation of an appropriate phase along the continuous part of the spectrum. In the process, the asymptotic properties of the Jost function as E→±m are analyzed in detail. The connection with the nonrelativistic version of Levinson’s theorem is also established.
    URI
    http://hdl.handle.net/10919/47071
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    • Scholarly Works, Department of Mathematics [245]

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