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21.
We show that the exact energy eigenvalues and eigenfunctions of the Schrödinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov–Bohm potentials as special cases. The results are in exact agreement with other methods. 相似文献
22.
We proposed a simple potential harmonic(PH) scheme for calculating the non-relativistic radial correlation energies of atomic systems.The scheme was applied to the low-lying n1S(n=1,2) and n3S(n=2,3) states of the helium atom.The results exhibit a very stable convergence characterization in both the angular and radial directions with PH and generalized Laguerre functions(GLF) respectively,even though the method is non-variational one.The ninth significant figure of the non-relativistic radial energy(NRE) calculated for the ground state exactly agrees with that of the most accurate literature data from the modified configuration interaction method.The convergent NRE′s for the excited states 21S,23S and 33S with the similar accuracy were also obtained. 相似文献
23.
Deformed soliton,breather,and rogue wave solutions of an inhomogeneous nonlinear Schrdinger equation 下载免费PDF全文
We use the 1-fold Darboux transformation (DT) of an inhomogeneous nonlinear Schro¨dinger equation (INLSE) to construct the deformed-soliton, breather, and rogue wave solutions explicitly. Furthermore, the obtained first-order deformed rogue wave solution, which is derived from the deformed breather solution through the Taylor expansion, is different from the known rogue wave solution of the nonlinear Schro¨dinger equation (NLSE). The effect of inhomogeneity is fully reflected in the variable height of the deformed soliton and the curved background of the deformed breather and rogue wave. By suitably adjusting the physical parameter, we show that a desired shape of the rogue wave can be generated. In particular, the newly constructed rogue wave can be reduced to the corresponding rogue wave of the nonlinear Schro¨dinger equation under a suitable parametric condition. 相似文献
24.
We give some multidimensional Tauberian theorems for generalized functions and show examples of their application in mathematical physics. In particular, we consider the problems of stabilizing the solutions of the Cauchy problem for the heat kernel equation, multicomponent gas diffusion, and the asymptotic Cauchy problem for a free Schrödinger equation in the norms of different Banach spaces among others. 相似文献
25.
Damian Trif 《Journal of mathematical chemistry》2008,43(3):1163-1176
The paper presents a Matlab package for the linear time-(in)dependent Schr?dinger equation, based on the Hermite spectral
method. The matrix form of the discretized problem is suitable for the linear algebra capabilities of Matlab. The high accuracy
and efficiency of the algorithm is proved by many examples taken from the literature.
相似文献
26.
Daniel Lenz Norbert Peyerimhoff Olaf Post Ivan Veselić 《Japanese Journal of Mathematics》2008,3(1):121-161
We first analyze the integrated density of states (IDS) of periodic Schrödinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with both continuous and discontinuous IDS. Subsequently, alloy-type perturbations of the periodic operator are considered. The randomness may enter both via the potential and the metric. A Wegner estimate is proven which implies the continuity of the corresponding IDS. This gives an example of a discontinuous “periodic” IDS which is regularized by a random perturbation. 相似文献
27.
Both original and twisted Schr?dinger-Virasoro algebras, and also their deformations were introduced and investigated in a
series of papers by Henkel, Roger and Unterberger. In the present paper we aim at determining the 2-cocycles of original deformative
Schr?dinger-Virasoro algebras.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 10471091, 10671027), Foundation of
Shanghai Education Committee (Grant No. 06FZ029) and “One Hundred Talents Program” from University of Science and Technology
of China 相似文献
28.
J. I. Abdullaev 《Theoretical and Mathematical Physics》2006,147(1):486-495
We consider the Hamiltonian of a system of two fermions on a one-dimensional integer lattice. We prove that the number of
bound states N(k) is a nondecreasing function of the total quasimomentum of the system k ∈ [0, π]. We describe the set of discontinuity points of N(k) and evaluate the jump N(k +0) − N(k) at the discontinuity points. We establish that the bound-state energy z
n
(k) increases as the total quasimomentum k ∈ [0, π] increases.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 1, pp. 47–57, April, 2006. 相似文献
29.
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