共查询到20条相似文献,搜索用时 109 毫秒
1.
氢原子和谐振子的能级、波函数的联系 总被引:1,自引:1,他引:0
求氢原子和谐振子的能级、波函数是解两个不同的定态薛定谔方程的问题。实际上,我们从三维谐振子的径向方程出发,应用适当的变换,就能由三维谐振子的能级和波函数导出氢原子与类氢离子的能级和波函数. 相似文献
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三维各向同性谐振子的守恒张量及其轨道方程 总被引:4,自引:0,他引:4
从牛顿第二定律出发,得到了三维各向同性谐振子的守恒张量,证明了守恒张量能提供一个独立的常数,并运用守恒张量的分量表示谐振子的运动方程,铁道平面方程,长轴和短轴所在直线方程及新坐标系下的轨道方程。 相似文献
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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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提出了一种新的类Quesne环状球谐振子势,应用二分量方法求解1/2-自旋粒子满足的Dirac方程, Dirac哈密顿量由标量和矢量类Quesne环状球谐振子势构成.在Σ=S(r)+V(r)=0的条件下,得到了Dirac旋量波函数下分量的束缚态解和能谱方程, 显示出类Quesne环状球谐振子势场中的赝自旋对称性.讨论了束缚态波函数和能谱方程的有关性质.
关键词:
类Quesne环状球谐振子势
Dirac方程
赝自旋对称性
束缚态 相似文献
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This paper establishes a new isospectral problem. By making use of
the Tu scheme, a new integrable system is obtained. It gives
integrable couplings of the system obtained. Finally, the Hamiltonian
form of a binary symmetric constrained flow of the system obtained is
presented. 相似文献
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Robert A. Van Gorder 《Physics letters. A》2008,372(31):5152-5158
In this Letter, we obtained solutions to a class of density dependent diffusion Nagumo equations. In particular, series solutions are obtained, along with a bound for the range of the convergence. Also, numerical solutions are obtained by the Runge-Kutta-Fehlberg 45 method. Moreover, the dependence of the traveling wave solutions on various parameters is discussed. Furthermore, we compare the series solutions with the numerical solutions to validate the numerical method. The results obtained in this study reveal many interesting behaviors that warrant further study on the Nagumo equation. 相似文献
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Duffing方程的变分迭代解法 总被引:1,自引:0,他引:1
应用变分迭代算法分析了Dufing方程的强迫振动,得到了整个区域内(0 < ε < ∞)一致有效的近似解,其近似周期的最大相对误差小于5.66%,并得到了在整个区域内一致有效的主共振和次共振频率。 相似文献
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XU Xi-Xiang 《理论物理通讯》2012,57(6):953-960
A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectic map and a completely integrable finite-dimensional Hamiltonian system. 相似文献
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对已知的Lie代数An-1作直接推广得到一类新的Lie代数gl(n,C).为应用方便,本文只考虑Lie代数gl(3,C)情形.构造了gl(3,C)的一个子代数,通过对阶数的规定,得到了一类新的loop代数.作为其应用,设计了一个新的等谱问题,得到了一个新的Lax对.利用屠格式获得了一族新的可积系统,具有双Hamilton结构,且是Liouville可积系.作为该方程族的约化情形,得到了新的耦合广义Schrdinger方程.
关键词:
Lie代数
可积系
Hamilton结构 相似文献
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Regularized oxygen concentration depth profiles were extracted from ARXPS data obtained on a plasma-oxidized polystyrene sample, using a variety of regulators and over a wide range of values for the regularization parameter. The plausibility of the profiles obtained was assessed with respect to strong and weak criteria based on a priori considerations. It was found that the most plausible results were obtained with regulators based upon the slopes or the curvatures exhibited in the profile. 相似文献
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Paolo Amore 《Annals of Physics》2010,325(12):2679-427
We obtain systematic approximations for the modes of vibration of a string of variable density, which is held fixed at its ends. These approximations are obtained iteratively applying three theorems which are proved in the paper and which hold regardless of the inhomogeneity of the string. Working on specific examples we obtain very accurate approximations which are compared both with the results of WKB method and with the numerical results obtained with a collocation approach. Finally, we show that the asymptotic behaviour of the energies of the string obtained with perturbation theory, worked to second order in the inhomogeneities, agrees with that obtained with the WKB method and implies a different functional dependence on the density that in two and higher dimensions. 相似文献
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《Journal of Nonlinear Mathematical Physics》2013,20(3):234-244
Abstract Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential equations. For the equations so obtained, first integrals are deduced which consequently give rise to explicit solutions. Potential symmetries, which are realized as local symmetries of a related auxiliary system, are obtained. For some special nonlinearities new symmetry reductions and exact solutions are derived by using the nonclassical method. 相似文献