VACUUM ENERGY IN SMOOTH BACKGROUND FIELDS

We consider the ground-state energy of a scalar held in the background of a general potential which depends on one coordinate. We consider a general expression following from the analytical properties of the on e-dimensional scattering matrix. We show that reflections give a posit ive and bound states a negative contribution to the ground-state energ y and we calculate explicitly two simple examples, the square-well pot ential and a piecewise oscillatory potential. We demonstrate our formu lae by an easy rederivation of the mass of the kink.