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