Advertisement

Levinson's theorem for the Klein-Gordon equation in one dimension

  • S.-H. Dong

Abstract:

In terms of the modified Sturm-Liouville theorem, the Levinson theorem for the one-dimensional Klein-Gordon equation with a symmetric potential V(x) is established. It is shown that the number N+ (N-) of bound states with even (odd) parity is related to the phase shift \(\) of the scattering states with the same parity at zero momentum as \(\) and \(\) The solution of the one-dimensional Klein-Gordon equation with the energy M or -M is called as a half bound state if it is finite but does not decay fast enough at infinity to be square integrable.

PACS. 03.65.Ge Solutions of wave equations: bound states - 11.80.-m Relativistic scattering theory - 73.50.Bk General theory, scattering mechanisms 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© EDP Sciences, Springer-Verlag, Società Italiana di Fisica 2000

Authors and Affiliations

  • S.-H. Dong
    • 1
  1. 1.Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, UK and Department of Physics, Cardwell Hall, Kansas State University, Manhattan, Kansas 66506, USAUS

Personalised recommendations