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谐振子薛定谔方程的简单解法 总被引:2,自引:0,他引:2
物质的许多物理与化学性质都可以用线性谐振子模型解释,本文用简单的数学运算求解线性谐振子的薛定谔方程,避免了特殊函数等复杂的数学运算,得出了量子力学教材完全相同的结果。 相似文献
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“薛定谔猫”—宏观量子叠加态 总被引:36,自引:1,他引:35
综述了近年来在量子光学方面关于“薛定谔猫”态的研究进展,包括其渊源,定义,制备,性质和可能的应用,“薛定谔猫”态本质上是两个宏观可区分的态相干叠加,它涉及量子力学的基本问题,对样一个问题进行研究,将有助于对量子力学的解释进行探讨。 相似文献
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通过构造哈密顿量与谐振子系统哈密顿量对易的超对称系统,量子谐振子的性质就可以通过对超对称系统的研究来得到.利用超对称系统的性质,在没有用到厄米多项式的情况下,给出了谐振子本征函数中展开系数间的递推关系,由递推关系可以直接得到本征函数.此方法下得到的归一化本征函数与用厄米多项式表达的本征函数完全相同,并且本征函数的宇称可以明显的显示出来. 相似文献
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用因式分解法求解薛定谔方程 总被引:3,自引:2,他引:1
利用德·拉·佩纳等人关于阶梯算符方法的表述形式,可以使因式分解法的步骤规范化,以利于在初等量子力学和量子化学教学中广泛应用.我们把这种方法应用于球坐标下的自由粒子、三维各向同性谐振子和二维氢原子,得到令人满意的结果. 相似文献
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求解定态薛定谔方程常常会涉及到常微分方程的本征值问题.目前解常微分方程本征值用的比较多的方法是以龙格-库塔方法为基础的打靶方法.打靶方法常用,但是计算时间长.当边界条件比较复杂或比较敏感的时候,用松弛法会有更好的效果.本文用松弛法解薛定谔方程,并和理论解进行比较.发现松弛法得到的数值解和理论解符合度很高,而且使用松弛法... 相似文献
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《Journal of Nonlinear Mathematical Physics》2013,20(2):207-233
The nonlinear Schrödinger equation is studied for a periodic sequence of delta-potentials (a delta-comb) or narrow Gaussian potentials. For the delta-comb the time-independent nonlinear Schrödinger equation can be solved analytically in terms of Jacobi elliptic functions and thus provides useful insight into the features of nonlinear stationary states of periodic potentials. Phenomena well-known from classical chaos are found, such as a bifurcation of periodic stationary states and a transition to spatial chaos. The relation to new features of nonlinear Bloch bands, such as looped and period doubled bands, are analyzed in detail. An analytic expression for the critical nonlinearity for the emergence of looped bands is derived. The results for the delta-comb are generalized to a more realistic potential consisting of a periodic sequence of narrow Gaussian peaks and the dynamical stability of periodic solutions in a Gaussian comb is discussed. 相似文献
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利用分离变量法,研究了(2+1)维非线性薛定谔(NLS)方程的局域结构.由于在B?cklund变换和变量分离步骤中引入了作为种子解的任意函数,得到了NLS方程丰富的局域结构.合适地选择任意函数,局域解可以是dromion,环孤子,呼吸子和瞬子.dromion解不仅可以存在于直线孤子的交叉点上,也可以存在于曲线孤子的最近邻点上.呼吸子在幅度和形状上都进行了呼吸
关键词:
非线性薛定谔方程
分离变量法
孤子结构 相似文献
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Axel Schulze-Halberg 《Foundations of Physics Letters》2002,15(6):585-589
Two results on the Schrödinger equation for a particle on the surface of a torus are obtained: In the first part of this note closed-form zero-energy solutions for a free particle are given. In the second part we show for which potentials depending only on the polar angle the Schrodinger equation becomes exactly solvable. 相似文献
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以大学物理的角度来介绍三种推导Black—Scholes期权定价方程的方法,并以,物理专业易于理解的方式来剖析相关的推导过程. 相似文献
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R S Kaushal 《Pramana》1994,42(4):315-318
The ground state of a class of potentials described byV(x)=a
20
x
2+a
1/x
2 is investigated. This potential possesses some distinct features like that of a symmetric double-well potential, and can
be used in modelling the fusion process of two identical nuclei as well. 相似文献
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By using the solutions of an auxiliary elliptic equation, a direct algebraic method is proposed to construct the exact solutions of nonlinear Schrfdinger type equations. It is shown that many exact periodic solutions of some nonlinear Schro^edinger type equations are explicitly obtained with the aid of symbolic computation, including corresponding envelope solitary and shock wave solutions. 相似文献
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Using the extended homogeneous balance method, we have obtained abundant exact solution structures of a (2+1)-dimensional integrable model, the Nizhnik--Novikov--Veselov equation. By means of leading order terms analysis, the nonlinear transformations of the Nizhnik--Novikov--Veselov equation are given first, and then some special types of single solitary wave solution and multisoliton-like solutions are constructed. 相似文献