On the spectra of Schrödinger operators

We give two formulas for the lowest point[Figure not available: see fulltext.] in the spectrum of the Schrödinger 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[Figure not available: see fulltext.] 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.