Scattering two-particle states of the sine-Gordon and sine-Gordon mode
ls in D + 1 dimensions are investigated for all values of the coupling
constant with the Gaussian wave-functional approach. In 1 + 1 and 2 1 dimensions, the phase shifts of the scattering states are obtained.
We find that the phase shifts are positive for the sine-Gordon field
theory and negative for the sinh-Gordon field theory. In the higher di
mensions, the phase shifts vanish, which is coincident with the trivia
lity of the two field theories.