Effective mass schrödinger equation for exactly solvable class of one-dimensional potentials

We deal with the exact solutions of Schr?dinger equation characterized by position-dependent effective mass via point canonical transformations. The Morse, P?schl-Teller, and Hulthén type potentials are considered, respectively. With the choice of position-dependent mass forms, exactly solvable target potentials are constructed. Their energy of the bound states and corresponding wavefunctions are determined exactly.      

一类Kdv非线性Schr(o|¨) dinger组合微分方程组的有限元分析

本文用有限元方法对一类kdv非线性schr(o|¨) dinger组合微分方程组进行数值分析,讨论了半离散、全离散有限元方法的误差估计和收敛阶。     

Rigorous Derivation of the Cubic NLS in Dimension One

We derive rigorously the one-dimensional cubic nonlinear Schrödinger equation from a many-body quantum dynamics. The interaction potential is rescaled through a weak-coupling limit together with a short-range one. We start from a factorized initial state, and prove propagation of chaos with the usual two-step procedure: in the former step, convergence of the solution of the BBGKY hierarchy associated to the many-body quantum system to a solution of the BBGKY hierarchy obtained from the cubic NLS by factorization is proven; in the latter, we show the uniqueness for the solution of the infinite BBGKY hierarchy.     

利用大失谐的Jaynes-Commings模型实现薛定谔猫态的隐形传态

提出了利用一个二能级原子与腔场的相互作用,通过大失谐的J-C模型来隐形传输腔场的薛定谔“猫态”的方案．在此方案中我们只需要一个二能级原子和两个单摸腔场,而不需要其他的辅助粒子．     

自锁模钛宝石激光器中的光谱调制和双脉冲运转

在自锁模钛宝石激光器中,除可形成传统的单脉冲外,在适当的条件下,还可产生双脉冲。本文运用广义脉宽公式单独计及棱镜系统的色散,用分步富氏法数值求解非线性薛定谔方程,在脉宽自洽的判据下,模拟了双脉冲的形成过程。结果表明,小量的净负色散配合强的啁啾是形成光谱调制的条件。双脉冲只产生在有限的参数范围内且极易被破坏。     

双环形氢原子势束缚态的精确解

若氢原子势被一个双环形状的平方反比势环绕,即称为双环形氢原子势。采用解析方法研究了双环形氢原子势束缚态的精确解,首先将双环形氢原子势的Schrdinger方程在球坐标系中进行分离变量,然后利用超几何方程和合流超几何方程求解角向方程和径向方程,给出了精确的能谱方程,获得了用超几何函数表示的归一化的角向波函数和用拉革尔多项式表示的归一化径向波函数。     

相敏光放大器对光纤偏振模色散进行补偿的探讨

根据耦合非线性薛定谔方程,在考虑偏振模色散的情况下,采用数值方法仿真了含有相敏光放大器的高速光纤传输系统性能,获得了一组优化参量.仿真结果表明,相敏光放大器对于光纤偏振模色散的影响有一定的补偿作用.     

Schrǒdinger方程特征值问题的Wilson元误差近似

讨论三维Schrǒdinger方程的特征值问题的Wilson元离散,并给出相应的误差估计．