Estimates for Eigenvalues of the Schrödinger Operator on Domains in Complete Noncompact Riemannian Manifolds
نویسندگان
چکیده
In this paper, we consider the eigenvalue problem of the Schrödinger operator, and obtain some universal inequalities for eigenvalues of the Schrödinger operator in complete simple connected noncompact Riemmannian manifolds admitting special functions which include hyperbolic space.
منابع مشابه
Universal Bounds for Eigenvalues of Schrödinger Operator on Riemannian Manifolds
Abstract. In this paper we consider eigenvalues of Schrödinger operator with a weight on compact Riemannian manifolds with boundary (possibly empty) and prove a general inequality for them. By using this inequality, we study eigenvalues of Schrödinger operator with a weight on compact domains in a unit sphere, a complex projective space and a minimal submanifold in a Euclidean space. We also st...
متن کاملSpectral Theory of Complete Riemannian Manifolds
A survey is presented about the spectrum of the Laplace operator on noncompact Riemannian manifolds. Topics include manifolds with purely continuous spectrum, eigenvalues embedded in the continuum, and spectral stability.
متن کاملThe Spectrum of Schrödinger Operators with Positive Potentials in Riemannian Manifolds
Let M be a noncompact complete Riemannian manifold. We consider the Schrödinger operator −∆ + V acting on L2(M), where V is a nonnegative, locally integrable function on M . We obtain some simple conditions which imply that inf Spec(−∆ + V ), the bottom of the spectrum of −∆ + V , is strictly positive. We also establish upper and lower bounds for the counting function N(λ).
متن کاملOperator-valued tensors on manifolds
In this paper we try to extend geometric concepts in the context of operator valued tensors. To this end, we aim to replace the field of scalars $ mathbb{R} $ by self-adjoint elements of a commutative $ C^star $-algebra, and reach an appropriate generalization of geometrical concepts on manifolds. First, we put forward the concept of operator-valued tensors and extend semi-Riemannian...
متن کاملGeometric Scattering Theory and Applications
Classical scattering theory, by which we mean the scattering of acoustic and electromagnetic waves and quantum particles, is a very old discipline with roots in mathematical physics. It has also become an important part of the modern theory of linear partial differential equations. Spectral geometry is a slightly more recent subject, the goal of which is to understand the connections between th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013