量子力学对称性

作者简介

这是一套由德国著名理论物理学家W．Griner教授编著的13卷集的理论物理学教科书。是一套内容完整的非常实用的从大学生到硕士研究生的现代物理学教材。它以系统的、统一的、连贯的方式阐述了现代理论物理学的诸方面。这套教材面世后，不仅在德国产生了巨大的影响，其英文版的及时推出，对全世界理论物理学的教学也起了很好的促进作用。

本套教材的特点是：①取材新颖。作者十分重视最新实验数据对理论物理学概念发展和深化的重要作用，不断引人大量新的材料扩充其内容。②内容叙述简明。清晰、易懂，数学推导详尽。③每卷中都输入了数以百计的例题和习题，并均给出了详细的解答。这在当前理物理学的大量出版物中是极为难得的，它能帮助和辅导学生把理论物理学的概念与方法应用于解决物理学家感兴趣的实验问题。④书中每章后附有与本章内容有关的科学家传略。这套风格风格一致、符号统一、前后连贯、内容全面的教材，不仅对理论物理专业的大学生、教师、研究生及研究人员是难得的好书，对广大爱好理论物理学的各方面人士也有很好的参考价值。

本书为英文版。

书籍目录

1. Symmetries in Quantum Mechanics  1.1  Symmetries in Classical Physics  1.2  Spatial Translations in Quantum Mechanics  1.3  The Unitary Translation Operator  1.4  The Equation of Motion for States Shifted in Space  1.5  Symmetry and Degeneracy of States  1.6  Time Displacements in Quantum Mechanics  1.7  Mathematical Supplement: Definition of a Group  1.8  Mathematical Supplement:Rotations and their Group Theoretical Properties   1.9  An Isomorphism of the Rotation Group  1.10   The Rotation Operator for Many-Particle States   1.11   Biographical Notes2. Angular Momentum Algebra Representation  of Angular Momentum Operators: Generators of SO(3)    2.1  Irreducible Representations of the Rotation Group  2.2  Matrix Representations of Angular Momentum Operators  2.3  Addition of Two Angular Momenta  2.4  Evaluation of Clebsch-Gordan Coefficients  2.5  Recursion Relations for Clebsch-Gordan Coefficients  2.6   Explicit Calculation of Clebsch-Gordan Coefficients   2.7  Biographical Notes3. Mathematical Supplement: Fundamental Properties of Lie Groups  3.1  General Structure of Lie Groups  3.2  Interpretation of Commutators as Generalized Vector Products, Lie's Theorem, Rank of Lie Group  3.3   Invariant Subgroups, Simple and Semisimple Lie Groups, Ideals  3.4  Compact Lie Groups and Lie Algebras  3.5  Invariant Operators (Casimir Operators)  3.6   Theorem of Racah  3.7   Comments on Multiplets  3.8   Invariance Under a Symmetry Group  3.9  Construction of the Invariant Operators  3.10  Remark on Casimir Operators of Abelian Lie Groups   3.11   Completeness Relation for Casimir Operators  3.12   Review of Some Groups and Their Propertiesand Transformations of Functions  3.14  Biographical Notes4.Symmetry Groups and Their Physical Meaning:General Considerations  4.1  Biographical Notes5.The lsospin Group (Isobaric Spin)   5.1  Isospin Operators for a Multi-Nucleon System   5.2  General Properties of Representations of a Lie Algebra    5.3  Regular (or Adjoint) Representation of a Lie Algebra   5.4  Transformation Law for Isospin Vectors   5.5  Experimental Test of Isospin lnvariance   5.6  Biographical Notes6.The Hypercharge   6.1  Biographical Notes7. The SU(3) Symmetry  7.1  The Groups U(n) and SU(n)  7.2  The Generators of SU(3)  7.3  The Lie Algebra of SU(3)  7.4  The Subalgebras of the SU(3) Lie Algebra and the Shift Operators  7.5  Coupling of T, U and V Multiplets   7.6  Quantitative Analysis of Our Reasoning  7.7  Further Remarks About the Geometric Form of an SU(3) Multiplet  7.8  The Number of States on Mesh Points on Inner Shells8.Quarks and SU(3)  8.1  Searching for Quarks  8.2  The Transformation Properties of Quark States  8.3  Construction of all SU(3) Multiplets from the Elementary Representations [3] and  8.4  Construction of the Representation D(p, q) from Quarks and Antiquarks  8.5  Meson Multiplets  8.6  Rules for the Reduction of Direct Products of SU(3) Multiplets  8.7  U-Spin Invariance  8.8  Test of U-Spin Invariance  ……9.Representations of the Permutation Group and Young Tableanx10.Mathematical Excursion Group Characters11.Charm and SU(4)12.Mathematical Supplement13.Special Discrdts Symmetries14.Dynamical Symmetries15.Mathematical Excursion:Non-compact Lie Gruoups16.Proff of Racah s TheoremSubject Index

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