ON THE SPECTRA OF SCHRODINGER-OPERATORS

We give two formulas for the lowest point T in the spectrum of the Schrodinger operator L = -(d/dt)p(d/dt) + q, where the coefficients p and q are real-valued, bounded, uniformly continuous functions on the real line. We determine whether or not T is an eigenvalue for L in terms of a set of probability measures on the maximal ideal space of the C*-algebra generated by the translations of p and q.