Discreteness of spectrum for the Schrödinger operators on manifolds of bounded geometry

  title={Discreteness of spectrum for the Schr{\"o}dinger operators on manifolds of bounded geometry},
  author={Vladimir Kondrat’ev and Mikhail Shubin},
We consider a Schrödinger operator H = −∆ + V (x) with a semi-bounded below potential V on a Riemannian manifold M of bounded geometry. A necessary and sufficient condition for the spectrum of H to be discrete is given in terms of V . It is formulated by use of the harmonic (Newtonian) capacity in geodesic coordinates on M . This extends the famous result… CONTINUE READING