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BK

Second edition

Weinheim : Wiley-VCH, [2020]

xvii, strana 924-1589 : ilustrace ; 25 cm

ISBN 978-3-527-34554-0 (vázáno)

francouzština

Obsahuje bibliografii na stranách 1545-1567, bibliografické odkazy a rejstřík

This textbook introduces concepts such as the quantum theory of scattering by a potential, special and general cases of adding angular momenta, time-independent and time-dependent perturbation theory, and systems of identical particles. The entire book has been revised to take into account new developments in quantum mechanics curricula. The textbook retains its original style in is new edition: fundamental concepts are explained in chapters, each followed by complements that provide more detailed discussions, examples and applications..

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VOLUME II // Table of contents v // VIII AN ELEMENTARY APPROACH TO THE QUANTUM THEORY OF SCATTERING BY A POTENTIAL 923 // A Introduction... 923 // B Stationary scattering states. Calculation of the cross section...928 // C Scattering by a central potential. Method of partial waves...941 // READER’S GUIDE FOR COMPLEMENTS 957 // Avin The free particle: stationary states // with well-defined angular momentum 959 // 1 The radial equation ...959 // 2 Free spherical waves...961 // 3 Relation between free spherical waves and plane waves...967 // Bviii Phenomenological description of collisions with absorption 971 // 1 Principle involved ...971 // 2 Calculation of the cross sections ...972 // ? Some simple applications of scattering theory 977 // 1 The Born approximation for a Yukawa potential...977 // 2 Low energy scattering by a hard sphere...980 // 3 Exercises...981 // IX ELECTRON SPIN 985 // A Introduction of electron spin ...986 // B Special properties of an angular momentum 1/2...990 // C Non-relativistic description of a spin 1/2 particle...991 // READER’S GUIDE FOR COMPLEMENTS 999 // Aix Rotation operators for a spin 1/2 particle 1001 // 1 Rotation operators in state space...1001 // 2 Rotation of spin states...1002 // 3 Rotation of two-component spinors...1005 // Bix // Exercises // 1009 // X ADDITION OF ANGULAR MOMENTA 1015 // A Introduction...1015 // B Addition of two spin 1/2’s. Elementary method...1019 // C Addition of two arbitrary angular momenta. General method...1025 // READER’S GUIDE FOR COMPLEMENTS 1041 // Ax Examples of addition of angular momenta 1043 // 1 Addition of ji = 1 and j2 = 1...1043 // 2 Addition of an integral orbital angular momentum l and a spin 1/2.1046 // Bx Clebsch-Gordan coefficients 1051 // 1 General properties of Clebsch-Gordan coefficients...1051 // 2 Phase conventions. Reality of Clebsch-Gordan coefficients...1054 //

3 Some useful relations...1056 // Cx Addition of spherical harmonics 1059 // 1 The functions (fix; fž2)...1059 // 2 The functions Fp(fž)...?60 // 3 Expansion of a product of spherical harmonics; the integral of a product of // three spherical harmonics...1062 // Dx Vector operators: the Wigner-Eckart theorem 1065 // 1 Definition of vector operators; examples...1066 // 2 The Wigner-Eckart theorem for vector operators...1067 // 3 Application: calculation of the Landé gj factor of an atomic level...1072 // Ex Electric multipole moments 1077 // 1 Definition of multipole moments...1077 // 2 Matrix elements of electric multipole moments...1084 // Fx Two angular momenta Ji and J2 coupled by // an interaction aJi • J2 1091 // 1 Classical review...1092 // 2 Quantum mechanical evolution of the average values (Ji) and (J2).1093 // 3 The special case of two spin 1/2’s...1095 // 4 Study of a simple model for the collision of two spin 1/2 particles...1102 // Gx Exercises 1107 // XI STATIONARY PERTURBATION THEORY 1115 // A Description of the method...1116 // ? Perturbation of a non-degenerate level...1120 // C Perturbation of a degenerate state...1124 // READER’S GUIDE FOR COMPLEMENTS 1129 // Axi A one-dimensional harmonic oscillator subjected to a perturbing // potential in x, x2, x3 1131 // 1 Perturbation by a linear potential ...1131 // 2 Perturbation by a quadratic potential...1133 // 3 Perturbation by a potential in x3...1135 // Bxi Interaction between the magnetic dipoles of two spin 1/2 // particles 1141 // 1 The interaction Hamiltonian W...1141 // 2 Effects of the dipole-dipole interaction on the Zeeman sublevels of two fixed // particles...1144 // 3 Effects of the interaction in a bound state...1149 // Cxi Van der Waals forces 1151 // 1 The electrostatic interaction Hamiltonian for two hydrogen atoms ...1152 // 2 Van der Waals forces between two hydrogen atoms in the Is ground state 1154 //

3 Van der Waals forces between a hydrogen atom in the Is state and a hydrogen // atom in the 2p state...1158 // 4 Interaction of a hydrogen atom in the ground state with a conducting wall. . 1160 // Dxi The volume effect: the influence of the spatial extension of the nucleus on the atomic levels 1162 // 1 First-order energy correction...1164 // 2 Application to some hydrogen-like systems...1166 // Exi The variational method 1169 // 1 Principle of the method...1169 // 2 Application to a simple example...1172 // 3 Discussion...1174 // Fxi Energy bands of electrons in solids: a simple model 1177 // 1 A first approach to the problem: qualitative discussion...1178 // 2 A more precise study using a simple model...1181 // Gxi A simple example of the chemical bond: the ion 1189 // 1 Introduction...1189 // 2 The variational calculation of the energies...1192 // 3 Critique of the preceding model. Possible improvements...1201 // 4 Other molecular orbitals of the Hj ion...1204 // 5 The origin of the chemical bond; the virial theorem...1210 // Hxi Exercises // 1221 // XII AN APPLICATION OF PERTURBATION THEORY: THE FINE AND HYPERFINE STRUCTURE OF THE HYDROGEN ATOM 1231 // A Introduction...1232 // ? Additional terms in the Hamiltonian...1233 // C The fine structure of the n = 2 level...1238 // D The hyperfine structure of the n = 1 level...1246 // E The Zeeman effect of the Is ground state hyperfine structure...1251 // READER’S GUIDE FOR COMPLEMENTS 1265 // Axu The magnetic hyperfine Hamiltonian 1267 // 1 Interaction of the electron with the scalar and vector potentials created by // the proton // 2 The detailed form of the hyperfine Hamiltonian...1268 // 3 Conclusion: the hyperfine-structure Hamiltonian...1274 // Bxh Calculation of the average values of the fine-structure Hamiltonian in the Is, 2s and 2p states 1276 // 1 Calculation of (l/R), (1/R2) and (1/R3)...1276 //

2 The average values (Wmv) . . . ...1278 // 3 The average values (Wd) ...1279 // 4 Calculation of the coefficient f2p associated with WSo in the 2p level..1279 // Cxh The hyperfine structure and the Zeeman effect for muonium and positronium 1281 // 1 The hyperfine structure of the Is ground state...1281 // 2 The Zeeman effect in the Is ground state...1282 // l>xii The influence of the electronic spin on the Zeeman effect of the hydrogen resonance line 1289 // 1 Introduction...1289 // 2 The Zeeman diagrams of the Is and 2s levels...1290 // 3 The Zeeman diagram of the 2p level...1290 // 4 The Zeeman effect of the resonance line...1293 // Exn The Stark effect for the hydrogen atom 1298 // 1 The Stark effect on the n = 1 level...1298 // 2 The Stark effect on the n = 2 level...1300 // XIII APPROXIMATION METHODS FOR TIME-DEPENDENT PROBLEMS 1303 // A Statement of the problem...1303 // ? Approximate solution of the Schrödinger equation...1305 // C An important special case: a sinusoidal or constant perturbation...1309 // D Random perturbation...1320 // E Long-time behavior for a two-level atom...1324 // Xll // READER’S GUIDE FOR COMPLEMENTS 1337 // Axiii Interaction of an atom with an electromagnetic wave 1339 // 1 The interaction Hamiltonian. Selection rules ...1340 // 2 Non-resonant excitation. Comparison with the elastically bound electron modell350 // 3 Resonant excitation. Absorption and induced emission...1353 // Bxin Linear and non-linear responses of a two-level system subject to a sinusoidal perturbation 1357 // 1 Description of the model...1358 // 2 The approximate solution of the Bloch equations of the system..1360 // 3 Discussion...1364 // 4 Exercises: applications of this complement...1372 // Cxin Oscillations of a system between two discrete states under the effect of a sinusoidal resonant perturbation 1374 // 1 The method: secular approximation...1374 //

2 Solution of the system of equations...1375 // 3 Discussion...1376 // Dxiii Decay of a discrete state resonantly coupled to a continuum of final states 1378 // 1 Statement of the problem...1378 // 2 Description of the model...1379 // 3 Short-time approximation. Relation to first-order perturbation theory ... 1383 // 4 Another approximate method for solving the Schrödinger equation...1385 // 5 Discussion...1386 // Exih Time-dependent random perturbation, relaxation 1390 // 1 Evolution of the density operator...1391 // 2 Relaxation of an ensemble of spin 1/2’s ...1398 // 3 Conclusion...1408 // Fxih Exercises 1409 // XIV SYSTEMS OF IDENTICAL PARTICLES 1419 // A Statement of the problem...1420 // ? Permutation operators...1425 // C The symmetrization postulate...1434 // D Discussion...1443 // READER’S GUIDE FOR COMPLEMENTS 1457 // Axiv Many-electron atoms. Electronic configurations 1459 // 1 The central-field approximation...1459 // 2 Electron configurations of various elements...1463 // Bxiv Energy levels of the helium atom. Configurations, terms, multiplets 1467 // 1 The central-field approximation. Configurations...1467 // 2 The effect of the inter-electron electrostatic repulsion: exchange energy, spec- // tral terms...1469 // 3 Fine-structure levels; multiplets...1478 // Cxiv Physical properties of an electron gas. Application to solids 1481 // 1 Free electrons enclosed in a box...1481 // 2 Electrons in solids...1491 // Dxiv Exercises 1496 // APPENDICES 1505 // I Fourier series and Fourier transforms 1505 // 1 Fourier series ...1505 // 2 Fourier transforms...1508 // II The Dirac  -“function” 1515 // 1 Introduction; principal properties...1515 // 2 The  -“function” and the Fourier transform...1520 // 3 Integral and derivatives of the 5-“function”...1521 // 4 The  -“function” in three-dimensional space...1524 //

III Lagrangian and Hamiltonian in classical mechanics 1527 // 1 Review of Newton’s laws...1527 // 2 The Lagrangian and Lagrange’s equations...1530 // 3 The classical Hamiltonian and the canonical equations...1531 // 4 Applications of the Hamiltonian formalism ...1533 // 5 The principle of least action...1539 // BIBLIOGRAPHY OF VOLUMES I AND II 1545 // INDEX 1569