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利用波函数及其导数的连续性条件,讨论Kronig—Penney模型中的电子波函数,得到Kronig—Penney模型相邻周期中波函数的转移矩阵,通过转移矩阵分析得到Kronig—Penney模型中的电子波函数,并进行了讨论. 相似文献
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闻小永 《原子与分子物理学报》2007,24(6):1171-1175
通过函数变换和扩展Jacobi椭圆函数展开法,利用吴消元法,借助符号运算软件Maple,得到非线性Schringer方程丰富的包络形式精确解,特别是由两个Jacobi椭圆函数表示的精确解.当模数m→1或m→0时,一部分解退化为双曲函数或三角函数表示的解,F-展开法和扩展的F-展开法得到的精确解是本文结果的特例. 相似文献
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Trial function method and exact solutions to the generalized nonlinear Schrodinger equation with time-dependent coefficient 下载免费PDF全文
In this paper, the trial function method is extended to study the generalized nonlinear Schrodinger equation with time- dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrodinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrodinger equation with time-dependent coefficients under constraint conditions. 相似文献
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将行波变换替换为更一般的函数变换,推广了修正的Jacobi椭圆函数展开方法.给出了非线性 Klein-Gordon方程新的周期解.当模m→1或m→0时,这些解退化成相应的孤立波解、三 角函数解和奇异的行波解.对于某些非线性方程,在一定条件下一般变换退化为行波约化.
关键词:
Jacobi椭圆函数
非线性发展方程
精确解 相似文献
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利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程.应用Jacobi椭圆函 数展开法求得了零级近似方程的准确解,并由此得到一级近似方程和二级近似方程分别满足 齐次Lam方程和非齐次Lam方程,应用Lam函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解.这样,就求得了非线性演化方程的多级准确解.
关键词:
Jacobi椭圆函数
Lam函数
多级准确解
非线性演化方程
扰动方法 相似文献
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We report on the generation of maximally localized photonic Wannier functions under constraints. This allows us to impress certain symmetry properties of the underlying Photonic Crystal onto the Wannier functions. This added flexibility enhances the utility of the Wannier function approach to Photonic Crystal circuits by providing deeper physical insight and making computations more efficient. 相似文献
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WANG Neng-Ping 《理论物理通讯》2011,55(1):158-170
I present a method to calculate the ballistic transport properties of atomic-scale structures under bias. The electronic structure of the system is calculated using the Kohn-Sham scheme of density functional theory (DFT). The DFT eigenvectors are then transformed into a set of maximally localized Wannier functions (MLWFs) [N. Marzari and D. Vanderbilt, Phys. Rev. B 56 (1997) 12847]. The MLWFs are used as a minimal basis set to obtain the Hamitonian matrices of the scattering region and the adjacent leads,which are needed for transport calculation using the nonequilibrium Green's function formalism. The coupling of the scattering region to the semi-infinite leads is described by the self-energies of the leads. Using the nonequilibrium Green's function method, one calculates self-consistently the charge distribution of the system under bias and evaluates the transmission and current through the system. To solve the Poisson equation within the scheme of MLWFs I introduce a computationally efficient method. The method is applied to a molecular hydrogen contact in two transition metal monatomic wires (Cu and Pt). It is found that for Pt the I-V characteristics is approximately linear dependence, however, for Cu the I-V characteristics manifests a linear dependence at low bias voltages and exhibits apparent nonlinearity at higher bias voltages. I have also calculated the transmission in the zero bias voltage limit for a single CO molecule adsorbed on Cu and Pt monatomic wires. While a chemical scissor effect occurs for the Cu monatomic wire with an adsorbed CO molecule, it is absent for the Pt monatomic wire due to the contribution of d-orbitals at the Fermi energy. 相似文献
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通过把十二个Jacobi椭圆函数分类成四组,提出了新的广泛的Jacobi椭圆函数展开法,利用这一方法求得了非线性发展方程的丰富的Jacobi椭圆函数双周期解.当模数m→0或1时,这些解退化为相应的三角函数解或孤立波解和冲击波解.
关键词:
非线性发展方程
Jacobi椭圆函数
双周期解
行波解 相似文献
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通过二维实映射研究非线性Kronig-Penney超晶格中的波输运特性,数值计算得到波矢一定情况下不同非线性系数的映射图、以及非线性系数一定情况下不同波矢的映射图.非线性Kronig-Penney超晶格中的非线性,对超晶格中波函数的Bloch波矢有明显的调节作用.随着非线性系数的增大,映射图由周期函数的有限个分立点变为准周期函数的一条闭合轨道、以及有规则或无规则的点分布.
关键词:
非线性Kronig-Penney超晶格
非线性效应
二维实映射
波矢 相似文献
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A hyperbolic function approach to constructing exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice 总被引:5,自引:0,他引:5 下载免费PDF全文
Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear
differential-difference equations. 相似文献
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In this paper, a two-step ansatz is proposed, which leads to some new solutions to two coupled nonlinear physical equations. 相似文献
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Exact travelling wave solutions to some nonlinear equations of fifth order derivatives are derived by using some accurate ansatz methods. 相似文献
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