The gap between the first two eigenvalues of Schrodinger operators with single-well potential

摘要

In this paper the Schrodinger operators endowed with Neumann or Dirichlet boundary conditions, where the potential q is an element of L-1[0, pi] is single-well with transition point a is an element of (0, pi), are considered. Suppose {nu(n)}(n >= 0) n and {lambda(n)}(n >= 1)) I are the set of eigenvalues for Neumann or Dirichlet problem, respectively, and the potential q(x) possesses an additional condition, we present estimates of lower bound for the differences nu(1) - nu(0) and lambda(2) - lambda(1), respectively. The results show that the energy transition for quantum particles jumping to the ground state is related to transition point is alpha.(C) 2015 Elsevier Inc. All rights reserved.