(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, USA, US
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.
Received 22 December 1999