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141.
Luobin FANG 《数学年刊B辑(英文版)》2020,41(2):227-240
In this paper, the author extends Peter Li and Tian Gang’s results on the heat kernel from projective varieties to analytic varieties. The author gets an upper bound of the heat kernel on analytic varieties and proves several properties. Moreover, the results are extended to vector bundles. The author also gets an upper bound of the heat operators of some Schr¨ondinger type operators on vector bundles. As a corollary, an upper bound of the trace of the heat operators is obtained. 相似文献
142.
A complete potential harmonic scheme is presented, including the linked coupled hyperradial ordinary differential equations and the secular equation of eigenenergy. It has been used to directly solve the Schrödinger equations of helium-like three-body systems (nuclear chargeZ = 1–9). and very accurate ground state eigenenergies as well as low-lying singlet excited state ones have been obtained. 相似文献
143.
144.
本文考虑了由最高峰的高度为m,并且峰的高度沿着Dyck路严格递增的所有Dyck路组成的集合,即集合Dm的子集的计数问题.利用双射、生成树以及Riordan阵的方法来对集合Dm的一些子集进行计数,得到了一些以经典的序列如Catalan数、Narayana数、Motzkin数、Fibonacci数、Schroder数以及第一类无符号Stirling数来计数的组合结构.特别地,我们给出了两个新的Catalan结构,它们并没有明显地出现在Stanley关于Catalan结构的列表中. 相似文献
145.
本文研究了分数阶薛定谔-泊松系统$$\left\{\begin{array}{l}(-\Delta)^su+u+\phi u=\lambda f(u)\ \text {in} \ \mathbb {R}^3, \\ (-\Delta)^{\alpha}\phi =u^2\ \text {in} \ \mathbb {R}^3\emph{},\end{array}\right. $$ 非零解的存在性, 其中$s\in (\frac{3}{4},1), \alpha\in(0,1),\lambda$ 是正参数, $(-\Delta)^s,(-\Delta)^{\alpha}$是分数阶拉普拉斯算子. 在一定的假设条件下, 利用扰动法和Morse迭代法, 得到了系统至少一个非平凡解. 相似文献
146.
147.
We discuss separability of solutions to a Schr?dinger equation that describes a composite quantum system and give some kinds of Hamiltonians H(t) such that the solution to Schr?dinger equation induced by H(t) is separable at any time provided that it is separable at t = 0. For example, we prove that if the Hamiltonian H is time-independent and equals to the product PA■PB of two projections on the subsystems KAand KB, respectively, then the state |ψ(t) of the composite system starting from a separable initial |ψ(0) = |ψA■|ψB is separable for all t ∈ [0, T] if and only if either |ψA is an eigenstate of PA, or |ψB is an eigenstate of PB. 相似文献
148.
本文研究了Hilbert空间L^2(R^2)上由势函数V(x)(V≥0,连续)给出的一类Schrǒdinger算子H=-△+V的谱。本文的主要结果:(1)H的谱σ(H)不会出现本性谱与离散谱交替出现的情况,其谱要么是离散的,要么从infσcos(H)开始全是本性谱;(2)lim‖x‖→∞V(x)=∞是σcos(H)=φ的充要条件。(3)借助于讨论H的Zhis-lin谱,在一定的条件下。lim‖x‖→∞V(x)=0是σcos(H)=[∞,0)的充要条件。我们还提出了几个没有解决的问题。 相似文献
149.
Standing wave solutions of the one-dimensional nonlinear Schrödinger equation with are well known to be unstable. In this paper we show that asymptotic stability can be achieved provided the perturbations of these standing waves are small and chosen to belong to a codimension one Lipschitz surface. Thus, we construct codimension one asymptotically stable manifolds for all supercritical NLS in one dimension. The considerably more difficult -critical case, for which one wishes to understand the conditional stability of the pseudo-conformal blow-up solutions, is studied in the authors' companion paper Non-generic blow-up solutions for the critical focusing NLS in 1-d, preprint, 2005.
150.
Yu. Kh. Eshkabilov 《Theoretical and Mathematical Physics》2006,149(2):1497-1511
In the space L 2(T ν ×T ν ), where T ν is a ν-dimensional torus, we study the spectral properties of the “three-particle” discrete Schrödinger operator ? = H0 + H1 + H2, where H0 is the operator of multiplication by a function and H1 and H2 are partial integral operators. We prove several theorems concerning the essential spectrum of ?. We study the discrete and essential spectra of the Hamiltonians Ht and h arising in the Hubbard model on the three-dimensional lattice. 相似文献