含时谐振子系统的时间演化及压缩态

研究了有压缩和驱动项的含时谐振子系统的时间演化.通过适当选取厄密不变量，得到含时谐振子系统的量子态时间演化的封闭解及该系统的时间演化算符，给出产生压缩态的条件，得出驱动项不影响系统压缩态的结论. 关键词：     

含时耦合谐振子系统的时间演化与双模压缩态

运用Lewis Riesenfeld不变量理论,通过适当地选取厄米不变量,得到了含驱动项和双模耦合项的含时耦合谐振子系统薛定谔方程的封闭解,给出了系统的演化算符及其产生双模光场的压缩态的条件,并得出系统压缩态的量子涨落与驱动项无关但与系统所处的初态有关的结论. 关键词： 含时耦合谐振子系统 Lewis Riesenfeld不变量理论 双模压缩态     

重夸克偶素的高阶变分-积分微扰修正

利用基于积分方程的改进的变分微扰方法(变分-积分微扰法)求解重夸克偶素激发态.设置含有变分参数的母哈密顿量作为零级哈密顿量,选择该母哈密顿系统的精确解作为试探波函数,得到了只有几项的高阶修正波函数和高阶能量修正.该计算结果更接近精确能量值,修正波函数的有界性和收敛性也得到了证明.结果表明,这种方法不仅可提高计算结果的精度,而且可确保微扰级数解的收敛性. 关键词： 重夸克偶素 变分-积分微扰法 高阶能量修正     

聚合物共混过程在线分析ARMA(p,q)模型的建立:小角光散射能量随时间变化的一维仿真研究

本文利用小角激光背散射 ( BSALS)在线分析系统对聚苯乙烯 ( PS)与顺丁橡胶( Pc BR)不相容体系共混过程中光散射强度 ( I( q)随时间的变化进行了分析 ,建立了自回归模型 ARMA( p,q) ,利用 AIC、BIC准则确定了模型的阶数 p和 q。用此模型对光散射强度进行模拟 ,经检验模拟结果与实验结果基本吻合。     

阻尼谐振子到简谐振子的变换

在牛顿力学、拉格朗日力学和哈密顿力学3种形式中,利用变量变换将阻尼谐振子变换成简谐振子.     

Quadrupole perturbation of the harmonic oscillator potential

TheSU(3) symmetry of the harmonic oscillator potential is used to calculate exactly the second order energy correction, caused by quadrupole deformations. This can be done in a purely algebraic manner, using the Dalgarno-Schwartz formulation of perturbation theory. Some connections of this method with group theory are discussed and an extension to more general situations is proposed.     

待定系数法求解一维线性谐振子在微扰体系下的解析解

本文应用待定系数法研究了电荷为q的线性谐振子受恒定电场作用下体系解析解的求解方法.     

Quantum normal form and the harmonic oscillator withx 6 perturbation

The eigenvalue problem of the harmonic oscillator with thex ⁶ perturbation,H=1/2(p ²+x ²+x ⁶), is investigated using the method of quantum normal form. The energy eigenvalues are found to be in good agreement with the WKB results.     

Path integration of the harmonic oscillator with a two-time quadratic action

Path integration of the harmonic oscillator with a two-time quadratic action characterizing memory effects is given in terms of the solutions of some integrodifferential equations. The exact propagator in closed form is then obtained for the specific kernel introduced by Feynman in the polaron problem.     

Higher energy levels of the harmonic oscillator and stochastic electrodynamics

Higher energy levels of the harmonic oscillator and the “radial quantification” formula for the hydrogen atom are obtained within the framework of stochastic electrodynamics. In two remarks, intricacies of quantum mechanics are highlighted.     

哈密顿算符的对角化与能量本征值问题的代数解法

提出了将哈密顿算符对角化的一种方法.围绕一维谐振子讨论了如何将哈密顿算符对角化、引进的是玻色算符还是费米算符的问题,并分析了能量量子化的原因及能量子与声子的区别.     

Exact and approximate solutions to the Schrödinger equation for the harmonic oscillator with a singular perturbation

I obtain exact solutions for the quantum-mechanical harmonic oscillator with a perturbation potential which belongs to a class of polynomial functions of 1/r. I show that some of the eigenfunctions enable the calculation of expectation values in closed form and are therefore suitable trial functions for the application of the variational method to related nonsolvable problems.