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Boundedness and convergence of perturbed corrections for helium-like ions in ground states 下载免费PDF全文
Applying the improved Rayleigh SchrSdinger perturbation theory based on an integral equation to helium-like ions in ground states and treating electron correlations as perturbations, we obtain the second-order corrections to wavefunctions consisting of a few terms and the third-order corrections to energicity. It is demonstrated that the corrected wavefunctions are bounded and quadratically integrable, and the corresponding perturbation series is convergent. The results clear off the previous distrust for the convergence in the quantum perturbation theory and show a reciprocal development on the quantum perturbation problem of the ground state helium-like systems. 相似文献
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Consider two magnetically coupled and perturbed long Josephson junctions which operate in synchronized modes. Under first order approximation, the soliton solution of the system is derived by using a new perturbation technique. It is shown that the perturbing parameters limit the emitted power from the system, and the physically relevant coupling parameter leads to the increase of power. The formula of maximal emitted power is given for a particular power input. The results solve some important problems left over by previous analysis. 相似文献
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We study exact single-soliton solutions of an attractive Bose-Einstein condensate governed by a one-dimensional nonautonomous Gross-Pitaevskii system. For several different forms of time-dependent atom-atom interaction and external parabolic potential which satisfy the exact integrability scenario, we construct a set of new analytical nonautonomous deformed-soliton solutions, including the macroscopic wave function and the position of soliton's center of mass. The soliton characteristics are modulated by the external field parameters and deformation factors related to the number of the condensed atoms and the initial conditions. The results suggest a simple and effective method for experimentally generating matter-wave deformed solitons and manipulating their motions. 相似文献
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考虑赝势近似下囚禁于Paul阱中的单离子与双δ脉冲型周期势相互作用系统的规则与混沌运动.应用积分方程方法得到系统的经典运动精确解,通过数值方法作出相空间轨道图和平均能量的时间演化曲线.结合分析与数值结果,发现两个有趣的结论.即在离子与单δ脉冲作用出现共振失稳的情形,在双δ脉冲作用下却出现了稳定的规则运动;离子随着双δ脉冲中两个脉冲之间的时间间隔减小而由规则运动转为混沌运动,其平均能量扩散的快慢与混沌运动的混乱程度相关.还研究了系统的共振失稳,发现通过调节激光波矢可以控制这种不稳定性. 相似文献
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无反射势阱的非齐次Schr(o)dinger方程的精确解 总被引:1,自引:0,他引:1
无反射势阱描述一种双原子分子的吸引势。将Rayleigh-Schrodinger展开法应用到微扰无反射势阱,得以一组非齐次Schrodinger方程。利用最近报道的微扰方法,导出这些方程的积分形式的精确解。以静电场与基态系统的相互作用为例,通过精确解的有界及其不能在Hilbert空间展开为有限项的性质,论证了该微扰系统束缚态的存在性及通常量子力学发散困难的起因。 相似文献
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Let σ and ρ be two field variables of the n-dimensional coupled scalar fields. Taking the function transformations σ=σ(ξ) and ρ=ρ(ξ) leads to an equation F(σ,ρ,dσ/dρ,d2σ/d2ρ) =0. Inserting any solution of this equation into the field equations yields a pair of general soliton solutions σ=σ(ξ) and ρ=ρ[σ(ξ)]. Some interesting specific soliton solutions are given. The stability and other properties of these solitons are discussed. 相似文献
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无反射势阱描述一种双原子分子的吸引势。将Rayleigh Schr dinger展开法应用到微扰无反射势阱 ,得到一组非齐次Schr dinger方程。利用最近报道的微扰方法 ,导出这些方程的积分形式的精确解。以静电场与基态系统的相互作用为例 ,通过精确解的有界及其不能在Hilbert空间展开为有限项的性质 ,论证了该微扰系统束缚态的存在性及通常量子力学发散困难的起因。 相似文献
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We investigate a one-dimensional open Bose-Einstein condensate with attractive interaction,by considering the effect of feeding from nonequilibrium thermal cloud and applying the time-periodic inverted-harmonic potential.Using the direct perturbation method and the exact shock wave solution of the stationary Gross-Pitaevskii equation,we obtain the chaotic perturbed solution and the Melnikov chaotic regions.Based on the analytical and the numerical methods,the influence of the feeding strength on the chaotic motion is revealed.It is shown that the chaotic regions could be enlarged by reducing the feeding strength and the increase of feeding strength plays a role in suppressing chaos.In the case of "nonpropagated" shock wave with fixed boundary,the number of condensed atoms increases faster as the feeding strength increases.However,for the free boundary the metastable shock wave with fixed front density oscillates its front position and atomic number aperiodically,and their amplitudes decay with the increase of the feeding strength. 相似文献