Variational Calculation of the Excited States in the Sing-Gordon and Sine-Gordon Field Theories

The one- and two-particle states in the sinh-Gordon and sine-Gordon models in (1+1) dimensions are investigated by using the gaussian wave-functional approach. We find that (i) the renormalized mass parameter is just the variational one particle mass, and (ii) there are no two-particle bound states in the sinh-Gordon model, but in the sine-Gordon model, there exist two-particle bound states.