N体Schrdinger算子势能的一些性质
Some Properties of Potential of a Class of N-body Schrdinger Operators
摘要
主要证明了一类N体Schrdinger算子的势能与常数Σcl的差的负部在无穷远处的衰减性,这个结果是研究N体Schrdinger算子离散谱个数的关键。
In this paper,the potentials of a class of N-body Schrdinger operators are studied.It is proved that the negative part of the difference of the potential and Σcl decays in the infinity.
出处
《河南科技大学学报(自然科学版)》
CAS
北大核心
2010年第4期78-80,共3页
Journal of Henan University of Science And Technology:Natural Science
基金
国家自然科学基金项目(50771042)
参考文献9
-
1Frohlich J, Graft S, Schwarz S. Mean-Field-and Classical Limit of Many-Body Schrodinger Dynamics for Bosons [J]. Commun Math Phys ,2007,271 ( 3 ) :681 - 697.
-
2Froese R G,Herbst I W. Exponential Bounds and Absence of Positive Eigenvalues for N-body Schrdinger Operators[ J ]. Commun Math Phys, 1982,87 ( 3 ) :429 - 447.
-
3Kitoda H. Asymptotic Completeness of N-Body wave Operators I: Short-Range Quantum Systems [ J ]. Reviews in Mathematical Physics, 1991,3 ( 1 ) : 101 - 124.
-
4Klaus M,Simon B. Coupling Constant Thresholds in non-relativistic Quantum Mechanics,II. Two Cluster Thresholds in N- Body Systems [ J ]. Commun Math Phys, 1980,78 ( 2 ) : 153 - 168.
-
5Benedetto D, Castella F, Esposito R, et al. From the N-body Schrodinger Equation to the Quantum Bohzmann Equation: a Term-by-Term Convergence Result in the Weak Coupling Regime[ J]. Commun Math Phys,2008,277 (1) :1 -44.
-
6Birman M Ah, Borzov V V. On the Asymptotics of the Discrete Spectrum of some Singular Operators[J]. Prob Math Phys, 1971(5) :24 -38.
-
7Tamura H. The Asymptotic Distribution of the Lower Part Eigenvalues for Elliptic Operators[ J]. Proc Japan Acad, 1974,50 (3) :185 - 187.
-
8Simon B. Classical Boundary Conditions as a Technical Tool in Modern Mathematical Physics [ J]. Adv in Math, 1978,30 (3) :268 -281.
-
9Reed M, Simon B. Methods of Modern Mathematical Physics, IV. Analysis of operators [ M ]. New York, London : Academic Press, 1978.
-
1贾小尧,赵丽英,任凤章.两类Schrdinger算子的关系[J].河南科技大学学报(自然科学版),2011,32(1):72-74.
-
2胡盛清,王硕.五体问题的中心构型及其相对平衡解[J].数学学报(中文版),2014,57(6):1199-1202.
-
3杨斌,阳名珠.一类积分——微分方程离散谱的存在性[J].数学物理学报(A辑),1990,10(1):80-84.
-
4吴平.某类系统离散谱的上界估计[J].宁波职业技术学院学报,2008,12(2):11-14. 被引量:3
-
5崔建莲,侯晋川.一类缺项算子矩阵正补的谱刻画[J].数学研究,1999,32(2):173-178.
-
6蒋志民.Volterra-Stieltjes微积分方程和算子[J].商丘师专学报,1999,15(2):57-60.
-
7王侃民,周军.关于一类微分算子的离散谱(英文)[J].工程数学学报,2003,20(1):71-76.
-
8陈祖墀.多调和算子组的谱估计(英文)[J].中国科学技术大学学报,1991,21(1):1-9.
-
9孙炯,王忠.常微分算子谱的定性分析[J].数学进展,1995,24(5):406-422. 被引量:31
-
10周立广,王万义,索建青.一类高阶微分算子谱的离散性的充分必要条件[J].系统科学与数学,2013,33(3):373-382. 被引量:3