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31.
Weak L
2
-solutions u of the Schrödinger equation, –u + q(x) u – u = f(x) in L
2
, are represented by a Fourier series using spherical harmonics in order to prove the following strong maximum and anti-maximum principles in
(N 2): Let 1 denote the positive eigenfunction associated with the principal eigenvalue 1 of the Schrödinger operator
. Assume that the potential q(x) is radially symmetric and grows fast enough near infinity, and f is a `sufficiently smooth' perturbation of a radially symmetric function, f 0 and 0 f / C const a.e. in
. Then u is 1-positive for - < < 1 (i.e., u c 1 with c const > 0) and 1-negative for 1 < < 1 + (i.e., u –c1 with c const > 0), where > 0 is a number depending on f. The constant c > 0 depends on both and f. 相似文献
32.
Michael Taylor 《Journal of Fourier Analysis and Applications》1999,5(5):449-463
We prove a number of results about pointwise convergence of eigenfunction expansions of functions on compact manifolds. In particular, we establish that the Pinsky phenomenon holds for piecewise smooth functions on the three-dimensional torus, with jump across the boundary of a ball, in the same form as it was discovered for functions on three-dimensional Euclidean space. Our work on this has been stimulated by recent work of Brandolini and Colzani, and we also discuss some variants of their results. 相似文献
33.
L.?BoultonEmail author S.?A.?M.?Marcantognini M.?D.?Morán 《Letters in Mathematical Physics》2004,70(2):121-131
We consider a vector-valued Hermite-type basis for which the eigenvalue problem associated to the operator H
A,B
:=B(;
x
2
)+Ax
2 acting on
becomes a three-terms recurrence. Here A and B are 2 × 2 constant positive definite matrices. Our main result provides an explicit characterization of the eigenvectors of H
A,B
that lie in the span of the first four elements of this basis when AB BA.This revised version was published online in March 2005 with corrections to the cover date. 相似文献
34.
In this Letter we develop a general procedure leading from a Mourre-type estimation for a given self-adjoint operator H to a Hardy-type weighted inequality. We use this method in order to prove exponential decay for eigenvectors of a large class of perturbations of operators of convolution with bounded analytic functions. 相似文献
35.
Relativistic treatment of the spin-zero particles subject to the second Poschl-Teller-like potential 下载免费PDF全文
The three-dimensional Klein-Gordon equation is solved for the case of equal vector and scalar second Poschl-Teller potential by proper approximation of the centrifugal term within the framework of the asymptotic iteration method. Energy eigenvalues and the corresponding wave function are obtained analytically. Eigenvalues are computed numerically for some values of n and It is found that the results are in good agreement with the findings of other methods for short-range potential. 相似文献
36.
The spin-weighted spheroidal equation in the case of s = 1 is studied. By transforming the independent variables, we make it take the Schrdinger-like form. This Schrdinger-like equation is very interesting in itself. We investigate it by using super-symmetric quantum mechanics and obtain the ground eigenvalue and eigenfunction, which are consistent with the results previously obtained. 相似文献
37.
WANG Wen-Ge 《理论物理通讯》2001,35(2):143-150
The Wigner band random matrix model is studied by making use of a generalization of Brillouin-Wigner perturbation theory. Energy eigenfunctions are shown to be divided into perturbative and nonperturbative parts. A relation between the average shape of eigenstates and that of the so-called local spectral density of states (LDOS) is derived by making use of some properties of energy eigenfunctions drawn from numerical results.
Several perturbation strengths predicted by the perturbation theory
are found to play important roles in the variation of the shape of the LDOS with perturbation strength. 相似文献
38.
The symplectic eigenfunction expansion theorem and its application to the plate bending equation 下载免费PDF全文
This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner. 相似文献
39.
40.
本文研究斜对角无穷维Hamilton算子$H=\begin{pmatrix}0&B\\C&0\end{pmatrix}$的点谱和特征函数系辛结构的非退化性, 给出斜对角无穷维Hamilton算子$H$的特征函数系具有非退化辛结构的充分必要条件. 基于此, 进一步刻画了斜对角无穷维Hamilton算子$H$的点谱分别包含于实轴、虚轴以及其它区域的充分必要条件. 最后, 以板弯曲问题和弦振动问题中导出的斜对角无穷维Hamilton算子为例, 验证了所得结论的正确性. 相似文献