SEMI-CLASSICAL LIMIT OF THE LOWEST EIGENVALUE OF A SCHRÖDINGER OPERATOR ON A WIENER SPACE : I. UNBOUNDED ONE PARTICLE HAMILTONIANS by
نویسنده
چکیده
— We study a semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. The Schrödinger operator is a perturbation of the second quantization operator of an unbounded self-adjoint operator by a C3-potential function. This result is an extension of [1].
منابع مشابه
Semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space : I. Unbounded one particle Hamiltonians
We study a semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. The Schrödinger operator is a perturbation of the second quantization operator of an unbounded self-adjoint operator by a C-potential function. This result is an extension of [1].
متن کاملSemiclassical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space Dedicated to Professor Tokuzo Shiga on the occasion of his sixtieth birthday
We study a semiclassical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. Key results are semiboundedness theorem of the Schrödinger operator, Laplace-type asymptotic formula and IMS localization formula. We also make a remark on semiclassical problem of a Schrödinger operator on a path space over a Riemannian manifold. MSC: Primary 81Q20, Secondary 60H07, 35J10.
متن کاملSemi-classical limit of the bottom of spectrum of a Schrödinger operator on a path space over a compact Riemannian manifold
We determine the limit of the bottom of spectrum of Schrödinger operators with variable coefficients on Wiener spaces and path spaces over finite dimensional compact Riemannian manifolds under semi-classical limit. These are extensions of the results in [4]. The problem on path spaces over Riemannian manifolds are considered as a problem on Wiener spaces by Ito’s map. However the coefficient op...
متن کاملThe Integrated Density of States and its Absolute Continuity for Magnetic Schrödinger Operators with Unbounded Random Potentials
The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schrödinger operator with magnetic field and unbounded random potential. In case of a constant magnetic field and an ergodic random potential, we prove the existence of the integrated density of states as the infinite-volume limit of suitable...
متن کاملSymmetry, Invariants, Topology in Molecules
The qualitative description of the system of energy levels of such quantum nite particle systems as molecules is largely based on the analysis of the classical symbols corresponding to eeective quantum Hamiltonians. The scheme of the qualitative analysis can be summarized as follows: Construction of the classical limit for a given model quantum Hamiltonian. This step includes the description of...
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 2009