Lectures on Quantum Mechanics - Assets

1 Lectures on Quantum MechanicsNobel Laureate Steven Weinberg combines his exceptional physical insight withhis gift for clear exposition to provide a concise introduction to modern suited to a one-year graduate course, this textbook is also a use-ful reference for researchers. Readers are introduced to the subject through areview of the history of Quantum Mechanics and an account of classic solu-tions of the Schr dinger equation, before Quantum Mechanics is developed ina modern Hilbert space approach. The textbook covers many topics not oftenfound in other books on the subject, including alternatives to the Copenhageninterpretation, Bloch waves and band structure, the Wigner Eckart theorem,magic numbers, isospin symmetry, the Dirac theory of constrained canonicalsystems, general scattering theory, the optical theorem, the in-in formalism,the Berry phase, Landau levels, entanglement, and Quantum computing.

2 Prob-lems are included at the ends of chapters, with solutions available for instructorsat WEINBERGis a member of the Physics and Astronomy Depart-ments at the University of Texas at Austin. His research has covered a broadrange of topics in Quantum field theory, elementary particle physics, and cosmol-ogy, and he has been honored with numerous awards, including the Nobel Prizein Physics, the National Medal of Science, and the Heinemann Prize in Math-ematical Physics. He is a member of the US National Academy of Sciences,Britain s Royal Society, and other academies in the USA and abroad. The Amer-ican Philosophical Society awarded him the Benjamin Franklin medal, with acitation that said he is considered by many to be the preeminent theoreticalphysicist alive in the world today. His books for physicists includeGravitationand Cosmology, the three-volume workThe Quantum Theory of Fields,andmost recently,Cosmology.

3 Educated at Cornell, Copenhagen, and Princeton,he also holds honorary degrees from sixteen other universities. He taught atColumbia, Berkeley, , and Harvard, where he was Higgins Professor ofPhysics, before coming to Texas in in this web service Cambridge University PressCambridge University Press978-1-107-02872-2 - Lectures on Quantum MechanicsSteven WeinbergFrontmatterMore in this web service Cambridge University PressCambridge University Press978-1-107-02872-2 - Lectures on Quantum MechanicsSteven WeinbergFrontmatterMore informationLectures on Quantum MechanicsSteven WeinbergThe University of Texas at in this web service Cambridge University PressCambridge University Press978-1-107-02872-2 - Lectures on Quantum MechanicsSteven WeinbergFrontmatterMore informationCAMBRIDGE UNIVERSITY PRESSC ambridge, New York, Melbourne, Madrid, Cape Town,Singapore, S o Paulo, Delhi.

4 Mexico CityCambridge University PressThe Edinburgh Building, Cambridge CB2 8RU, UKPublished in the United States of America by Cambridge University Press, New on this S. Weinberg 2013 This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place without the writtenpermission of Cambridge University published 2013 Printed and bound in the United Kingdom by the MPG Books GroupA catalog record for this publication is available from the British LibraryLibrary of Congress Cataloging in Publication dataWeinberg, Steven, 1933 Lectures on Quantum Mechanics / Steven 978-1-107-02872-2 (hardback)1. Quantum theory. I. dc232012030441 ISBN 978-1-107-02872-2 HardbackAdditional resources for this publication at University Press has no responsibility for the persistence oraccuracy of URLs for external or third-party internet websites referred toin this publication, and does not guarantee that any content on suchwebsites is, or will remain, accurate or in this web service Cambridge University PressCambridge University Press978-1-107-02872-2 - Lectures on Quantum MechanicsSteven WeinbergFrontmatterMore informationFor Louise, Elizabeth.

5 And in this web service Cambridge University PressCambridge University Press978-1-107-02872-2 - Lectures on Quantum MechanicsSteven WeinbergFrontmatterMore in this web service Cambridge University PressCambridge University Press978-1-107-02872-2 - Lectures on Quantum MechanicsSteven WeinbergFrontmatterMore informationContentsPREFACE pagexvNOTATION xviii1 HISTORICAL Photons1 Black-body radiation Rayleigh Jeans formula Planck formula Atomic constants Photoelectric effect Compton Atomic Spectra5 Discovery of atomic nuclei Ritz combination principle Bohr quantization condition Hydrogen spectrum Atomic numbers Sommerfeld quantization condition Wave Mechanics11De Broglie waves Davisson Germer experiment Schr Matrix Mechanics14 Radiative transition rate Harmonic oscillator Heisenberg matrix algebra Commutation relations Equivalence to wave Probabilistic Interpretation21 Scattering Probability density Expectation values Classical motion Born rulefor transition probabilitiesHistorical in this web service Cambridge University PressCambridge University Press978-1-107-02872-2 - Lectures on Quantum MechanicsSteven WeinbergFrontmatterMore informationviiiContents2 PARTICLE STATES IN A CENTRAL Schr dinger Equation for a Central Potential29 Hamiltonian for central potentials Orbital angular momentum operators SpectrumofL2 Separation of wave function Boundary Spherical Harmonics36 Spectrum ofL3 Associated Legendre polynomials Constructionof spherical harmonics Orthonormality The Hydrogen Atom39 Radial Schr dinger

6 Equation Power series solution Laguerre polynomials Energy levels Selection The Two-Body Problem44 Reduced mass Relative and center-of-mass coordinates Relative and total momenta Hydrogen and deuterium The Harmonic Oscillator45 Separation of wave function Raising and lowering operators Spectrum Normalized wave functions Radiative transition matrix elementsProblems503 GENERAL PRINCIPLES OF Quantum States52 Hilbert space Vector spaces Norms Completeness and independence Orthonormalization Probabilities Rays Dirac Continuum States58 From discrete to continuum states Normalization Delta functions Observables61 Operators Adjoints Matrix representation Eigenvalues Complete-ness of eigenvectors Schwarz inequality Uncertainty principle Dyads Projection operators Density matrix von Neumann Symmetries69 Unitary operators Wigner s theorem Antiunitary operators Continuous symme-tries Space Translation73 Momentum operators Commutation rules Momentum eigenstates Bloch waves Band in this web service Cambridge University PressCambridge University Press978-1-107-02872-2 - Lectures on Quantum MechanicsSteven WeinbergFrontmatterMore Time Translation77 Hamiltonians Time-dependent Schr dinger equation Conservation laws Timereversal Galilean invariance Boost Interpretations of Quantum Mechanics81 Copenhagen interpretation Two classes of interpretation Many-worlds interpreta-tions Examples of measurement Decoherence Calculation of probabilities Abandoning realism Decoherent histories interpretationProblems964 SPINET Rotations99

7 Finite rotations Action on physical states Infinitesimal rotations Commutationrelations Total angular momentum Angular Momentum Multiplets104 Raising and lowering operators Spectrum ofJ2andJ3 Spin matrices Paulimatrices J3-independence Stern Gerlach Addition of Angular Momenta109 Choice of basis Clebsch Gordan coefficients Sum rules Hydrogen states SU(2) The Wigner Eckart Theorem118 Operator transformation properties Theorem for matrix elements Parallel matrixelements Photon emission selection Bosons and Fermions121 Symmetrical and antisymmetrical states Connection with spin Hartree approxi-mation Pauli exclusion principle Periodic table for atoms Magic numbers fornuclei Temperature and chemical potential Statistics Insulators, conductors, Internal Symmetries131 Charge symmetry Isotopic spin symmetry Pions s Strangeness U(1)symmetries SU(3) Inversions138 Space Inversion Orbital parity Intrinsic parity Parity of pions Violations ofparity conservation P,C, Algebraic Derivation of the Hydrogen Spectrum142 Runge Lenz vector SO(3) SO(3)

8 Commutation relations Energy levels Scattering in this web service Cambridge University PressCambridge University Press978-1-107-02872-2 - Lectures on Quantum MechanicsSteven WeinbergFrontmatterMore informationxContents5 APPROXIMATIONS FOR ENERGY First-Order Perturbation Theory148 Energy shift Dealing with degeneracy State vector perturbation A The Zeeman Effect152 Gyromagnetic ratio Land g-factor SodiumDlines Normal and anomalousZeeman effect Paschen Back The First-Order Stark Effect157 Mixing of 2s1/2and 2p1/2states Energy shift for weak fields Energy shift forstrong Second-Order Perturbation Theory160 Energy shift Ultraviolet and infrared divergences Closure approximation Second-order Stark The Variational Method162 Upper bound on ground state energy Approximation to state vectors Virial theorem Other The Born Oppenheimer Approximation165 Reduced Hamiltonian Hellmann Feynman theorem Estimate of corrections Electronic, vibrational.

9 And rotational modes Effective The WKB Approximation171 Approximate solutions Validity conditions Turning points Energy eigenvalues one dimension Energy eigenvalues three Broken Symmetry179 Approximate solutions for thick barriers Energy splitting Decoherence Oscilla-tions Chiral moleculesProblems1816 APPROXIMATIONS FOR TIME-DEPENDENT First-Order Perturbation Theory183 Differential equation for amplitudes Approximate Monochromatic Perturbations184 Transition rate Fermi golden rule Continuum final Ionization by an Electromagnetic Wave187 Nature of perturbation Conditions on frequency Ionization rate of hydrogen in this web service Cambridge University PressCambridge University Press978-1-107-02872-2 - Lectures on Quantum MechanicsSteven WeinbergFrontmatterMore Fluctuating Perturbations189 Stationary fluctuations Correlation function Transition Absorption and Stimulated Emission of Radiation191 Dipole approximation Transition rates Energy density of radiation B-coefficients Spontaneous transition The Adiabatic Approximation193 Slowly varying Hamiltonians Dynamical phase Non-dynamical phase Degener-ate The Berry Phase196 Geometric character of the non-dynamical phase Closed curves in parameter space General formula for the Berry phase Spin in a slowly varying magnetic fieldProblems2027 POTENTIAL In-States203 Wave packets Lippmann Schwinger equation Wave packets at early times Spread of wave Scattering Amplitudes208 Green s function for scattering Definition of scattering amplitude Wave

10 Packet atlate times Differential The Optical Theorem211 Derivation of theorem Conservation of probability Diffraction The Born Approximation214 First-order scattering amplitude Scattering by shielded Coulomb Phase Shifts216 Partial wave expansion of plane wave Partial wave expansion of in wave function Partial wave expansion of scattering amplitude Scattering cross-section Scatteringlength and effective Resonances220 Thick barriers Breit Wigner formula Decay rate Alpha decay Ramsauer Townsend Time Delay224 Wigner formula Levinson s Theorem226 Conservation of discrete states Growth of phase in this web service Cambridge University PressCambridge University Press978-1-107-02872-2 - Lectures on Quantum MechanicsSteven WeinbergFrontmatterMore Coulomb Scattering227 Separation of wave function Kummer functions Scattering The Eikonal Approximation229 WKB approximation in three dimensions Initial surface Ray paths Calculationof phase Calculation of amplitude Application to potential scatteringProblems2348 GENERAL SCATTERING The S-Matrix235 In and out stat