共查询到18条相似文献,搜索用时 203 毫秒
1.
2.
研究多种正幂势函数与逆幂势函数紧密耦合条件下薛定谔径向方程解析解的求解方法.对势函数为V(r)=α1r8+α2r3+α3r2+β3r-1+β2r-3+β1r-4的径向薛定谔方程存在解析解的条件以及精确的解析解进行了研究. 根据量子系统波函数必须满足单值、有界和连续的标准条件,首先求出径向坐标r→∞以及r→0时的渐近解,然后采用非正则奇点邻域附近的波函数级数解法与求得的渐近解相结合,通过幂级数系数比较法得到径向薛定谔方程在势函数系数紧密耦合条件下的一系列定态波函数解析解以及相应的能级结构,并作适当讨论与结论.
关键词:
级数解法
幂势函数
径向波函数
渐近解 相似文献
3.
采用转化法.可得到一系列具有球对称势函数的径向Schrodinger方程的解析解和能级方程.这种方法是用一个恰当的尝试波函数代入Schrodinger方程后,将微分方程变成简单的可解的代数方程组,由此大大简化了运算.本文给出了库仑势、库仑势与谐振子势的叠加势以及离子与原子相互作用势的径向Schrodinger方程解析解,并得到能级方程.由于此方法中涉及一个势参数制约关系,为此以叠加势V(r)=-A1r-1-A2r-3+A3r-4为例,讨论其基态能级.得出重要结论:在库仑势上叠加上两项逆幂指数势作用后基态能量将增大,但是并不是单调增大,而是与各项势参数有关. 相似文献
4.
采用转化法.可得到一系列具有球对称势函数的径向Schr dinger方程的解析解和能级方程.这种方法是用一个恰当的尝试波函数代入Schr dinger方程后,将微分方程变成简单的可解的代数方程组,由此大大简化了运算.本文给出了库仑势、库仑势与谐振子势的叠加势以及离子与原子相互作用势的径向Schr dinger方程解析解,并得到能级方程.由于此方法中涉及一个势参数制约关系,为此以叠加势V(r)=-A1r-1-A2r-3+A3r-4为例,讨论其基态能级.得出重要结论:在库仑势上叠加上两项逆幂指数势作用后基态能量将增大,但是并不是单调增大,而是与各项势参数有关. 相似文献
5.
采用转化法,可得到一系列具有球对称势函数的径向Schroedinger方程的解析解和能级方程。这种方法是用一个恰当的尝试波函数代入Schroedinger方程后,将微分方程变成简单的可解的代数方程组,由此大大简化了运算。本给出了库仑势、库仑势与谐振子势的叠加势以及离子与原子相互作用势的径向Schroedinger方程解析解,并得到能级方程。由于此方法中涉及一个势参数制约关系,为此以叠加势V(r)=-A1r^-1-A2R^-3 A3r^-4为例,讨论其基态能级。得出重要结论:在库仑势上叠加上两项逆幂指数势作用后基态能量将增大,但是并不是单调增大,而是与各项势参数有关。 相似文献
6.
7.
一种简捷求解定态薛定谔方程的方法:科尔-霍普夫变换法 总被引:1,自引:0,他引:1
介绍一种求解各个能级及定态波函数的简捷方法,即借助于科尔-霍普夫(Cole-Hopf)变换法,将给定势函数的定态薛定谔方程变换成黎卡提(Riccati)方程,以求出各个能级及定态波函数.并以谐振子、球谐振子、氢原子、P schl-Teller势、Morse势、Hulth啨n势、双原子分子的三参量势函数、同调谐振子为实例,给出求解方法及结果. 相似文献
8.
9.
本文介绍求某些非线性演化方程的孤子解的投影矩阵方法,以求解非线性薛定谔方程为例来说明。 相似文献
10.
利用Poisson括号的正则不变性求得了Liouville方程的八类精确解:1)“重力”势系统,2)谐振系统,3)正负平方幂函数势系统,4)双曲函数势系统,5)三角函数势系统,6)PschlTeller势系统,7)“引(斥)力”势系统和8)Kratzer势系统.得到了“化动量正则变换”的一般方法.在求解后两个系统Liouville方程的过程中还应用了Routh方法和Binet方法.
关键词: 相似文献
11.
12.
13.
By applying Lou's direct perturbation method to perturbed nonlinear Schr(o)dinger equation and the critical nonlinear Schr(o)dinger equation with a small dispersion, their approximate analytical solutions including the zero-order and the first-order solutions are obtained. Based on these approximate solutions, the analytical forms of parameters of solitons are expressed and the effects of perturbations on solitons are briefly analyzed at the same time. In addition, the perturbed nonlinear Schr(o)dinger equations is directly simulated by split-step Fourier method to check the validity of the direct perturbation method. It turns out that the analytical results given by the direct perturbation method are well supported by numerical calculations. 相似文献
14.
高阶非线性薛定谔方程的精确周期解和孤波解 总被引:1,自引:1,他引:0
本文利用行波约化方法,研究了用于描述飞秒光脉冲传输的高阶非线性薛定谔方程,得到了它的包络型Jacobian椭圆函数双周期解和孤波解.分析结果表明亮孤子的存在依赖于负三阶色散效应,暗孤子的存在依赖于正三阶色散效应. 相似文献
15.
16.
Investigation of analytical harmonic frequency and potential energy function,vibrational levels for the X^2∑^+ and A^2Л states of CN radical 下载免费PDF全文
This paper calculates the equilibrium structure and the potential energy functions of the ground state (X^2∑^+) and the low lying excited electronic state (A^2Л) of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency (ωe) and other spectroscopic constants (ωeχe, βe and αe) are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function. 相似文献
17.
Using the formalism of supersymmetric quantum mechanics, we give an exact solution for a family of one-dimensional periodic potentials, which are the supersymmetric partners of the potential proportional to the trigonometric function cos(2x) such that the Schr?dinger equation for this potential is named the Mathieu equation mathematically. We show that the new potentials are distinctly different from their original ones. However, both have the same energy band structure. All the potentials obtained in this paper are free of singularities. 相似文献
18.
A. A. Rajabi 《Few-Body Systems》2006,40(1-2):21-33
The bound-state solutions to the hyperradial Schr?dinger equation is constructed for any general case comprising any hypercentral
power and inverse-power potentials. The hypercentral potential depends only on the hyperradius which itself is a function
of Jacobi relative coordinates that are functions of particle positions (r
1,r
2, … , and r
N
). This paper is mainly devoted to the demonstration of the fact that any ψ of the form ψ = power series × exp(polynomial)
= [f(x) exp (g(x))] is potentially a solution of the Schr?dinger equation, where the polynomial g(x) is an ansatz depending on the interaction potential. 相似文献