Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4626334 | Applied Mathematics and Computation | 2015 | 9 Pages |
Abstract
In this paper the Schrödinger operators endowed with Neumann or Dirichlet boundary conditions, where the potential q ∈ L1[0, π] is single-well with transition point a ∈ (0, π), are considered. Suppose {νn}n ≥ 0 and {λn}n ≥ 1 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 ν1−ν0ν1−ν0 and λ2−λ1,λ2−λ1, respectively. The results show that the energy transition for quantum particles jumping to the ground state is related to transition point a.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Xiu-Juan Yu, Chuan-Fu Yang,