Symmetry and condensed matter physics : a computational approach

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Symmetry and condensed matter physics : a computational approach / Michael El-Batanouny, M. El-Batanouny, Michael (Boston University) El-Batanouny, F. Wooten, Frederick Wooten

資料種別:

電子ブック

出版情報:

Cambridge University Press Online Books
2008

著者名:

ISBN:

9780521828451 [0521828457]
9786611370558 [6611370552]
9780521535526 [0521535522]

書誌ID:

OB00232333

子書誌情報

フルテキスト

所蔵情報

書誌詳細

その他の標題:

SYMMETRY AND CONDENSED MATTER PHYSICS
SYMMETRY & CONDENSED MATTER PHYSICS : A COMPUTATIONAL APPROACH

主題:

Physics - General and Others

言語:

英語

目次情報:

Preface

Symmetry and physics / 1：

Introduction / 1.1：

Hamiltonians, eigenfunctions, and eigenvalues / 1.2：

Symmetry operators and operator algebra / 1.3：

Point-symmetry operations / 1.4：

Applications to quantum mechanics / 1.5：

Exercises

Symmetry and group theory / 2：

Groups and their realizations / 2.1：

The symmetric group / 2.2：

Computational aspects / 2.3：

Classes / 2.4：

Homomorphism, isomorphism, and automorphism / 2.5：

Direct- or outer-product groups / 2.6：

Group representations: concepts / 3：

Representations and realizations / 3.1：

Generation of representations on a set of basis functions / 3.2：

Group representations: formalism and methodology / 4：

Matrix representations / 4.1：

Character of a matrix representation / 4.2：

Burnside's method / 4.3：

Computational projects

Dixon's method for computing group characters / 5：

The eigenvalue equation modulo p / 5.1：

Dixon's method for irreducible characters / 5.2：

Computer codes for Dixon's method / 5.3：

Finding eigenvalues and eigenvectors / Appendix 1：

Appendix 2

Computation project

Group action and symmetry projection operators / 6：

Group action / 6.1：

Symmetry projection operators / 6.2：

The regular projection matrices: the simple characteristic / 6.3：

Construction of the irreducible representations / 7：

Eigenvectors of the regular Rep / 7.1：

The symmetry structure of the regular Rep eigenvectors / 7.2：

Symmetry projection on regular Rep eigenvectors / 7.3：

Computer construction of Irreps with d[subscript alpha] > 1 / 7.4：

Summary of the method / 7.5：

Exercise

Product groups and product representations / 8：

Subgroups and cosets / 8.1：

Direct outer-product groups / 8.3：

Semidirect product groups / 8.4：

Direct inner-product groups and their representations / 8.5：

Product representations and the Clebsch-Gordan series / 8.6：

Computer codes / 8.7：

Summary / 8.8：

Induced representations / 9：

Subduced Reps and compatibility relations / 9.1：

Induction of group Reps from the Irreps of its subgroups / 9.3：

Irreps induced from invariant subgroups / 9.4：

Examples of Irrep induction using the method of little-groups / 9.5：

Frobenius reciprocity theorem and other useful theorems / Appendix：

Crystallographic symmetry and space-groups / 10：

Euclidean space / 10.1：

Crystallography / 10.2：

The perfect crystal / 10.3：

Space-group operations: the Seitz operators / 10.4：

Symmorphic and nonsymmorphic space-groups / 10.5：

Site-symmetries and the Wyckoff notation / 10.6：

Fourier space crystallography / 10.7：

Space-groups: Irreps / 11：

Irreps of the translation group / 11.1：

Induction of Irreps of space-groups / 11.2：

Time-reversal symmetry: color groups and the Onsager relations / 12：

The time-reversal operator in quantum mechanics / 12.1：

Spin-1/2 and double-groups / 12.3：

Magnetic and color groups / 12.4：

The time-reversed representation: theory of corepresentations / 12.5：

Theory of crystal fields / 12.6：

Onsager reciprocity theorem (Onsager relations) and transport properties / 12.7：

Tensors and tensor fields / 13：

Tensors and their space-time symmetries / 13.1：

Construction of symmetry-adapted tensors / 13.2：

Description and classification of matter tensors / 13.3：

Tensor field representations / 13.4：

Electronic properties of solids / 14：

The one-electron approximations and self-consistent-field theories / 14.1：

Methods and techniques for band structure calculations / 14.3：

Electronic structure of magnetically ordered systems / 14.4：

Derivation of the Hartree-Fock equations

Holstein-Primakoff (HP) operators / Appendix 2：

Dynamical properties of molecules, solids, and surfaces / 15：

Dynamical properties of molecules / 15.1：

Dynamical properties of solids / 15.3：

Dynamical properties of surfaces / 15.4：

Coulomb interactions and the method of Ewald summations

Electronic effects on phonons in insulators and semiconductors

Experimental measurements and selection rules / 16：

Selection rules / 16.1：

Differential scattering cross-sections in the Born approximation / 16.3：

Light scattering spectroscopies / 16.4：

Photoemission and dipole selection rules / 16.5：

Neutron and atom scattering spectroscopies / 16.6：

Landau's theory of phase transitions / 17：

Phase transitions and their classification / 17.1：

Landau theory of phase transitions: principles / 17.2：

Construction and minimization techniques for [Delta phi] / 17.3：

Incommensurate systems and quasi-crystals / 18：

The concept of higher-dimensional spaces: superspaces and superlattices / 18.1：

Quasi-crystal symmetry: the notion of indistinguishability and the classification of space-groups / 18.3：

Two-dimensional lattices, cyclotomic integers, and axial stacking / 18.4：

Bibliography

References

Index

Preface

Symmetry and physics / 1：

Introduction / 1.1：

Hamiltonians, eigenfunctions, and eigenvalues / 1.2：

Symmetry operators and operator algebra / 1.3：

Point-symmetry operations / 1.4：

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