相对论量子力学_百度百科
相对论量子力学
相对论（跟媒介有关），基本的，C=C0/K1+C1*K2 ,C为原地球速度，K1=地球线速度/（宇宙密度*普朗克加量-逃逸差量） C1为光线的变动密分速度。K2为 宇宙常量-地球水密度流 。相对论 量子力学 公式。 E=(E0+sqr（cm-K1） ）*B /(C0-M相对） 。
《相对论量子力学》是一部介绍相对论量子理论的研究生教程，重在强调其在凝聚态物理中的重要应用。基本理论包括：狭义相对论，角动量和零自旋粒子；文章讨论了Dirac 方程，对称和算子以及自由粒子，黑洞和Klein矛盾也被提及，并且解决了一些模型问题；紧接着主要量子理论在凝聚态物质中的应用，单电子原子爆炸的相对理论，并将该理论发展来描述多粒子系统的量子力学，包括Hartree-Fock和密度函数法。散射理论，带结构，磁光效应和超导。书中配有不少练习题。
1 The Theory of Special Relativity
1.1 The Lorentz Transformations
1.2 Relativistic Velocities
1.3 Mass, Momentum and Energy
1.4 Four-Vectors
1.5 Relativity and Electromagnetism
1.6 The Compton Effect
1.7 Problems
2 Aspects of Angular Momentum
2.1 Various Angular Momenta
2.2 Angular Momentum and Rotations
2.3 Operators and Eigenvectors for Spin 1/2
2.4 Operators for Higher Spins
2.5 Orbital Magnetic Moments
2.6 Spin Without Relativity
2.7 Thomas Precession
2.8 The Pauli Equation in a Central Potential
2.9 Dirac Notation
2.10 Clebsch-Gordan and Racah Coefficients
2.11 Relativistic Quantum Numbers and Spin-Angular Functions
2.12 Energy Levels of the One-Electron Atom
2.13 Plane Wave Expansions
2.14 Problems
3 Particles of Spin Zero
3.1 The Klein-Gordon Equation
3.2 Relativistic Wavefunctions, Probabilities and Currents
3.3 The Fine Structure Constant
3.4 The Two-Component Klein-Gordon Equation
3.5 Free Klein-Gordon Particles/Antiparticles
3.6 The Klein Paradox
3.7 The Radial Klein-Gordon Equation
3.8 The Spinless Electron Atom
3.9 Problems
4 The Dirac Equation
4.1 The Origin of the Dirac Equation
4.2 The Dirac Matrices
4.3 Lorentz Invariance of the Dirac Equation
4.4 The Non-Relativistic Limit of the Dirac Equation
4.5 An Alternative Formulation of the Dirac Equation
4.6 Probabilities and Currents
4.7 Gordon Decomposition
4.8 Forces and Fields
4.9 Gauge Invariance and the Dirac Equation
4.10 Problems
5 Free PaNicles/Antiparticles
5.1 Wavefunctions, Densities and Currents
5.2 Free-Particle Solutions
5.3 Free-Particle Spin
Rotations and Spinors
A Generalized Spin Operator
5.4 Negative Energy States, Antiparticles
5.5 Classical Negative Energy Particles?
5.6 The Klein Paradox Revisited
5.7 Lorentz Transformation of the Free-Particle Wavefunction
5.8 Problems
6 Symmetries and Operators
6.1 Non-Relativistic Spin Projection Operators
6.2 Relativistic Energy and Spin Projection Operators
6.3 Charge Conjugation
6.4 &lime-Reversal Invariance
6.5 Parity
6.7 Angular Momentum Again
6.8 Non-Relativistic Limits Again
6.9 Second Quantization
6.10 Field Operators
6.11 Second Quantization in Relativistic Quantum Mechanics
6.12 Problems
7 Separating Particles from Antiparticles
7.1 The Foldy-Wouthuysen Transformation for a Free Particle
7.2 Foldy-Wouthuysen Transformation of Operators
7.3 Zitterbewegung
7.4 Foldy-Wouthuysen Transformation of the Wavefunction
7.5 The F-W Transformation in an Electromagnetic Field
7.6 Problems
8 One-Electron Atoms
8.1 The Radial Dirac Equation
8.2 Free-Electron Solutions
8.3 One-Electron Atoms, Eigenvectors and Eigenvalues
8.4 Behaviour of the Radial Functions
8.5 The Zeeman Effect
8.6 Magnetic Dichroism
8.7 Problems
9 Potential Problems
9.1 A Particle in a One-Dimensional Well
9.2 The Dirac Oscillator
The Non-Relativistic Limit
Solution of the Dirac Oscillator
Expectation Values and the Uncertainty Principle
9.3 Bloch's Theorem
9.4 The Relativistic Kronig-Penney Model
A One-Dimensional Time-Independent Dirac Equation
A Potential Step
A One-Dimensional Solid
9.5 An Electron in Crossed Electric and Magnetic Fields
An Electron in a Constant Magnetic Field
An Electron in a Field for which
9.6 Non-Linear Dirac Equations, the Dirac Soliton
9.7 Problems
10 More Than One Electron
10.1 The Breit Interaction
10.2 Two Electrons
10.3 Many-Electron Wavefunctions
10.4 The Many-Electron Hamiltonian
10.5 Dirac-Hartree-Fock Integrals
Single-Particle Integrals
Two-Particle Integrals
The Direct Coulomb Integral
The Exchange Integral
10.6 The Dirac-Hartree-Fock Equations
The One-Electron Atom
The Many-Electron Atom
10.7 Koopmans' Theorem
10.8 Implementation of the Dirac-Hartree-Fock Method
10.9 Introduction to Density Functional Theory
10.10 Non-Relativistic Density Functional Theory
10.11 The Variational Principle and the Kohn-Sham Equation
10.12 Density Functional Theory and Magnetism
Density Functional Theory in a Weak Magnetic Field
Density Functional Theory in a Strong Magnetic Field
10.13 The Exchange-Correlation Energy
10.14 Relativistic Density Functional Theory (RDFT)
RDFT with an External Scalar Potential
RDFT with an External Vector Potential
The Dirac-Kohn-Sham Equation
10.15 An Approximate Relativistic Density Functional Theory
10.16 Further Development of RDFT
10.17 Relativistic Exchange-Correlation Functionals
10.18 Implementation of RDFT
11 Scattering Theory
11.1 Green's Functions
11.2 Time-Dependent Green's Functions
11.3 The T-Operator
11.4 The Relativistic Free-Particle Green's Function
11.5 The Scattered Particle Wavefunction
11.6 The Scattering Experiment
11.7 Single-Site Scattering in Zero Field
11.8 Radial Dirac Equation in a Magnetic Field
11.9 Single-Site Scattering in a Magnetic Field
11.10 The Single-Site Scattering Green's Function
11.11 Transforming Between Representations
11.12 The Scattering Path Operator
11.13 The Non-Relativistic Free Particle Green's Function
11.14 Multiple Scattering Theory
11.15 The Multiple Scattering Green's Function
11.16 The Average T-Matrix Approximation
11.17 The Calculation of Observables
The Band Structure
The Fermi Surface
The Density of States
The Charge Density
Magnetic Moments
Energetic Quantities
11.18 Magnetic Anisotropy
The Non-Relativistic Limit, the RKKY Interaction
The Orion of Anisotropy
12 Electrons and Photons
12.1 Photon Polarization and Angular Momentum
12.2 Quantizing the Electromagnetic Field
12.3 Time-Dependent Perturbation Theory
12.4 Photon Absorption and Emission in Condensed Matter
12.5 Magneto-Optical Effects
12.6 Photon Scattering Theory
12.7 Thomson Scattering
12.8 Rayleigh Scattering
12.9 Compton Scattering
12.10 Magnetic Scattering of X-Rays
12.11 Resonant Scattering of X-Rays
13 Superconductivity
13.1 Do Electrons Find Each Other Attractive?
13.2 Superconductivity, the Hamiltonian
13.3 The Dirac——Bogolubov-de Gennes Equation
13.4 Solution of the Dirac-Bogolubov-de Gennes Equations
13.5 Observable Properties of Superconductors
13.6 Elcctrodynamics of Superconductors
Appendix A The Uncertainty Principle
Appendix B The Confluent Hypergeometrie Function
B.1 Relations to Other Functions
Appendix C Spherical Harmonics
Appendix D Unit Systems
Appendix E Fundamental Constants
References工具类服务
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求解矩阵特征值和特征向量的PSO算法
提出一种基于粒子群优化算法的求解方法,将线性方程组的求解转化为无约束优化问题加以解决,采用粒子群优化算法求解矩阵特征值和特征向量.仿真实验结果表明,该方法求解精度高、收敛速度快,能够在10代左右收敛,可以有效获得任意矩阵的特征值和特征向量.
Abstract：
A method based on Particle Swarm Optimization(PSO)algorithm is presented,which transfers the equations into a non-constraint optimization problem.The PSO algorithm is used to solve matrix eigenvahes and eigenvectors.Simulation experimental results show the accuracy and the convergence speed of this method is higher,which can converge in about ten generations.It can obtain any matrix eigenvalues and eigenvectors.
WEI Xing-qiong
ZHOU Yong-quan
作者单位：
广西民族大学数学与计算机科学学院,南宁,530006
年，卷(期)：
Keywords：
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在线出版日期：
基金项目：
国家自然科学基金，国家民委科研项目，广西自然科学基金
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求翻译：eigenvalues and the corresponding eigenvectors是什么意思？
eigenvalues and the corresponding eigenvectors
问题补充：
特征值和相应的特征向量
相应的特征值和pdsyev
本征值和对应的特征向量
特征值和对应的特征向量
本征值和相应本征向量
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1Xy = λFyTThus the eigenvalues and eigenvectors of the scores ofindividuals can be obtained, among which we determine p largepositive
eigenvalues
1> λ1 ≥ λ2 ≥L≥ λp > 0
thecorresponding eigenvectors are y1, y2,Lyp. Thus the scores ofvariables and individuals in group p will be obtained. E = (a1, a2 L, ap)m× p Y = (y1, y2,L, yp)n× p
从而得到此样品得分的特征值和特征向量，我们在其中找 p 个小于1 的大特征值　 1>λ1 ≥ λ2 ≥L≥λp >0　　相应的特征向量为　　 y1, y2,Lyp　这样得到 p 组变量得分和样品得分，E = (a1, a2 L, ap)m 　　Y = (y1, y2,L, yp)n× p
The inverse eigenvalue problem of constructing centroskew symmetric matrices M,C,and K of size n for the quadratic pencil Q(λ)=λ~2M+λC+K so that Q(λ) has a prescribed subset of eigenvalues and eigenvectors is considered by singular value decomposition of matrix.
利用矩阵的奇异值分解,讨论构造n阶中心斜对称矩阵M,C和K,使得二次束Q(λ)=λ2M+λC+K具有给定特征值和特征向量的特征值反问题.
We summed up the conclusions of finding the eigenvalues and the eigenvectors of A~(-1), (transpose) matrix A~T, adjoint matrix A~*,P~(-1)AP and polynomial φ(A) from the eigenvalues and the eigenvectors of A at first.
首先对由 A的特征值、特征向量求 A- 1 ,AT,A* ( A的伴随矩阵 )、P- 1 AP以及 A的多项式φ( A)的特征值和特征向量的结论作了个归纳 ;
The Lanczos method in the calculation of eigenvectors derivatives
特征向量导数计算的Lanczos方法
MUSIC-like algorithms only use the eigenvectors of data matrix to estimate signal parameters without making full use of the information of
(3)MUSIC类算法和ESPRIT类算法都没有充分地利用特征值和特征向量中所包含的信息，MUSIC类算法只是使用特征向量估计参数而ESPRIT类算法只是使用特征值估计参数。
For any inner product of vectors W and X,there exists eigenvectors,γ
2 which coplanar with both of W and X,such that ｜γ
2｜2=?ni=1w
证明了对任意两向量 W和 X的内积 W·X= ni=1 wixi,存在两个与 W和 X共面的向量 ︽1 和 ︽2 使得 :|︽1 |2 =|︽2 |2 = ni=1 wixi=W· X.
After getting theeigenvalues and the eigenvectors of Hamiltont: H_0 = -gL_1→·L_2→ + λL~3_2 。 We find theeigenvectors of this model are muti-degenerate states.
我们在得到哈密顿量为:H_0= -gL_1→·L_2 +λL~3_2的系统的能量本征值及能量本征态之后,发现它的本征态是多重简并的。
is a finite subgroup of
(4),we will get the eigenvectors on noncommutative Orbifold
当G是SO(4)的有限子群时候它们是R4 /G这种非对易Orbifold上的态矢量 .
EIGENVECTORS OF NONLINEAR INTEGRAL OPERATORS OF HAMMERSTEIN TYPE
Hammerstein型非线性积分算子的固有元
Using topological degree theory researches some properties of eigenvectors of nonlinear Complete continuous operators, thereby generalizes classical Krein-Rutman theorem, and applies the obtained result to Hammerstein nonlinear integral equations.
用拓扑度理论研究非线性全连续算子固有元的性质,推广了经典Krein-Rutman定理,应用于非线性Hammerstein型积分方程。
Eigenvectors of Fuzzy Matrices
模糊矩阵的特征向量
PERTURBATION THEOREMS OF EIGENVECTORS
特征向量的几个扰动定理
查询“eigenvectors”译词为用户自定义的双语例句&&&&我想查看译文中含有：的双语例句
为了更好的帮助您理解掌握查询词或其译词在地道英语中的实际用法，我们为您准备了出自英文原文的大量英语例句，供您参考。&&&&&&&&&&&&&&&&&&&& By introducing the "reciprocal basic vectors" in nonorthogonal basic space, orthogonal and closure theorems are established. These theorems constitute the basis for symmetry analysis in molecular orbital methods. Symmetry analysis is used directly to determine the molecular orbitals,
eigenVectors of vibration and matrices of irreducible representation of cubic symmetric molecules. It may be used to study the effect of molecular deformation or vibration on molecular orbitals. Associated with Extended ... &&&&&&&&&&&&在非正交基空间中，引入“逆基矢量”，建立了正交性与完全性定理，因而提供了对称性分析的基本方法，并对分子轨道方法进行了讨论。 通过对称性分析，直接导出了立方对称分子的分子轨道，振动的本征矢量及对称元素不可约表示矩阵，它可以研究分子变形或振动对分子轨道的影响，与推广的Ｈüｃｋｅｌ法（ＫＨ）或自洽场Ｘα散射波（ＳＣＦ－Ｘα－ＳＷ）方法结合可以更好地研究大分子、固体的缺陷杂质和表面等问题。&&&&&&&& Let be an n×n partitioned matrix, where Aij(i,j = 1, 2, …n) are m×m matr-ices, is an n×n matrix, where λ_(ij)~((r))is an eigenvalue of Aij corresponding tocommon eigenvectorer. In this paper, the connection between eigenvolues, eigenvectors andJordan contextures of A and Q_A~((r)), and the connection between ||Ak||and and the acquired results have beenapllied to numerical methods in the differential equations. Someestablished concepts and inferences have been generalized。 &&&&&&&&&&&&设是n×n阶分块矩阵,其中Aij(1,J=1,2…n)为m×m阶矩阵,是n×n阶矩阵,其中λ_(ij)~((r))为Aij的相应于共同特征向量e_r的特征值。本文讨论了A和Q_A~((r))的特征值、特征同量、Jordan结构之间的关系以及‖A~k‖和‖(Q_A~((R)))~k‖之间的关系,并把所得结果应用到微分方程数值方法中、推广了某些原有要领和结论。&&&&&&&& This paper provides an efficient algorithm for finding all the eigenvalues and partial eigenvectors of a real matrix.Double QR step is used to find all the eigenvalue when the eigenvalues are known, inverse iteration is used to compute the selected eigenvector. &&&&&&&&&&&&本文提供求实矩阵全部特征值及部分特征矢量的一个富有成效的算法。求实矩阵的全部特征值用的是二重QR步骤;当特征值求出后.计算挑选的特征矢量用的是反迭代。&nbsp&&&&&&&&相关查询:
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