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1.
本文讨论了在实轴上具有紧支集的势的薛定谔算子的极点散射问题. 本文旨在将狄利克雷级数理论与散射理论相结合, 文中运用了Littlewood的经典方法得到关于极点个数的新的估计. 本文首次将狄利克雷级数方法用于极点估计, 由此得到了极点个数的上界与下界, 这些结果改进和推广了该论题的一些相关结论.  相似文献   
2.
本文研究了加权Banach空间中指数函数系完备的稳定性问题.利用解析函数扰动的方法,获得了加权Banach空间中指数函数系完备的稳定性若干结果,推广了现有有限区间Banach空间上的经典结果.  相似文献   
3.
张金平  程新路  张红  杨向东 《中国物理 B》2011,20(6):60401-060401
Three low-lying electronic states (x1+,a3+,and A1) of NO+ ion are studied using the complete active space self-consistent-field (CASSCF) method followed by highly accurate valence internally contracted multi-reference configuration interaction (MRCI) approach in combination of the correlation-consistent sextuple basis set augmented with diffuse functions, aug-cc-pV6Z. The potential energy curves (PECs) of the NO+(x1+,a3+,A1) are calculated. Based on the PECs, the spectroscopic parameters Re, De, ωe, ωeχe, α e, Be, and D0 are reproduced, which are in excellent agreement with the available measurements. By numerically solving the radial Schrödinger equation of nuclear motion using the Numerov method, the first 20 vibrational levels, inertial rotation and centrifugal distortion constants of NO+(x1+,a3+,A1) ion are derived when the rotational quantum number J is equal to zero (J = 0) for the first time, which accord well with the available measurements. Finally, the analytical potential energy functions of these states are fitted, which are used to accurately derive the first 20 classical turning points when J = 0. These results are compared in detail with those of previous investigations reported in the literature.  相似文献   
4.
本文用量子力学从头算方法深入研究了He原子与O2分子的相互作用势,选定CCSD(T)/6-311++G(3df,2pd)方法和基组,同时采用了Boys和Bernardi提出的Full Couterpoise方法消除了计算中的基组重叠误差(BSSE),得出了该体系的各向异性相互作用势的单点能数据,通过拟合得到了较为准确的He-O2体系相互作用势的解析表达式.采用精确度较高的密耦(Close-Coupling)近似方法,计算了He-O2碰撞体系的碰撞激发微分截面,计算得到的微分截面数据与实验值符合较好,并得出了不同碰撞能量时He原子与O2分子的碰撞的微分截面的规律.  相似文献   
5.
Using Vanderbilt-type plane-wave ultrasoft pseudopotentials within the generalized gradient approximation(GGA) in the frame of density functional theory(DFT),we have investigated the crystal structures,elastic,and thermodynamic properties for Ti2SC under high temperature and high pressure.The calculated pressure dependence of the lattice volume is in excellent agreement with the experimental results.The calculated structural parameter of the Ti atom experienced a subtle increase with applied pressures and the increase suspended under higher pressures.The elastic constants calculations demonstrated that the crystal lattice is still stable up to 200 GPa.Investigations on the elastic properties show that the c axis is stiffer than the a axis,which is consistent with the larger longitudinal elastic constants(C 33,C 11) relative to transverse ones(C 44,C 12,C 13).Study on Poisson's ratio confirmed that the higher ionic or weaker covalent contribution in intra-atomic bonding for Ti2SC should be assumed and the nature of ionic increased with pressure.The ratio(B/G) of bulk(B) and shear(G) moduli as well as B/C 44 demonstrated the brittleness of Ti2SC at ambient conditions and the brittleness decreased with pressure.Moreover,the isothermal and adiabatic bulk moduli displayed opposite temperature dependence under different pressures.Again,we observed that the Debye temperature and Gru篓neisen parameter show weak temperature dependence relative to the thermal expansion coefficient,entropy,and heat capacity,from which the pressure effects are clearly seen.  相似文献   
6.
顾建兵  杨向东  王怀谦  李慧芳 《中国物理 B》2012,21(4):43102-043102
The geometrical structures, relative stabilities, electronic and magnetic properties of small B n Al (2 ≤ n ≤ 9) clusters are systematically investigated by using the first-principles density functional theory. The results show that the Al atom prefers to reside either on the outer-side or above the surface, but not in the centre of the clusters in all of the most stable B n Al (2 ≤ n ≤ 9) isomers and the one excess electron is strong enough to modify the geometries of some specific sizes of the neutral clusters. All the results of the analysis for the fragmentation energies, the second-order difference of energies, and the highest occupied-lowest unoccupied molecular orbital energy gaps show that B 4 Al and B 8 Al clusters each have a higher relative stability. Especially, the B 8 Al cluster has the most enhanced chemical stability. Furthermore, both the local magnetic moments and the total magnetic moments display a pronounced odd-even oscillation with the number of boron atoms, and the magnetic effects arise mainly from the boron atoms except for the B 7 Al and B 9 Al clusters.  相似文献   
7.
沈光先  汪荣凯  令狐荣锋  杨向东 《物理学报》2011,60(1):13101-013101
采用超分子单双迭代(包括非迭代三重激发)耦合簇理论CCSD(T)方法,选择由原子中心高斯函数和高斯键函数3s3p2d1f组成的大基组,计算了He-H2(D2,T2)碰撞体系的H2分子取不同键长时的相互作用势能面.运用Tang-Toennies势模型和非线性最小二乘法拟合构造了He与同位素分子H2(D2,T2)在质心坐标系下的振转相互作用势.通过密耦计算得 关键词: 高斯键函数 Tang-Toennies势函数 分波截面 碰撞参数  相似文献   
8.
By using the B3P86/aug-cc-pvtz method,the accurate equilibrium geometry of the AlSO(CS,X2A″) molecule has been calculated and compared with available theoretical values.The obtained results show that the AlSO molecule has a most stable structure with bond lengths of R OAl = 0.1864 nm,R OS = 0.1623 nm,R AlS = 0.2450 nm,together with a dissociation energy of 13.88 eV.The possible electronic states and their reasonable dissociation limits for the ground state of the AlSO molecule were determined based on the principle of atomic and molecular reaction statics.The analytic potential energy function of the AlSO molecule was derived by the many-body expansion theory and the contour lines were constructed for the first time,which show the internal information of the AlSO molecule,including the equilibrium structure and stable point.The analysis demonstrates that the obtained potential energy function of AlSO is reasonable and successful and the present investigations provide important insights for further study on molecular reaction dynamics.  相似文献   
9.
杨向东 《物理学进展》2011,4(4):550-563
本文回顾了原子碰撞方面的研究工作,评述了近年来这一领域中的若干进展。目前原子碰撞的研究成果已被广泛应用到化学动力学、气体激光器、激光同位素分离、重离子加速器等方面。本文讨论了慢电子被原子散射的物理模型。考虑到在入射电子作用下靶原子的极化效应,入射电子与靶原子的电子间的交换作用和入射电子波的畸变,得到了入射电子与靶原子相互作用的解析势能函数,并讨论了氦、氩、锂、钠等原子对慢电子散射的最近研究成果。  相似文献   
10.
本文用高精度的量子力学ab initio方法计算了氦原子与一氧化碳分子相互作用各向异性势能面,通过三重激发校正耦合簇、二次组态相互作用等方法和不同基组的计算结果比较,并采用BSSE方法消除了基组重叠误差,得到了氦原子与一氧化碳分子体系相互作用各向异性势,然后采用精确度较高的密耦(Close-Coupling)近似方法,研究了氦原子与一氧化碳分子碰撞的散射截面,通过计算得出了该体系碰撞激发微分截面和分波截面,计算得到的微分截面数据与实验值符合较好,说明本文得到的势能面是准确的.  相似文献   
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