vPrefaceto the Revised EditionIn addition to the acknowledgments above, my former students LiPing,Shi Xiaohong, and Yasunaga Suzuki provided the sounding boardfor ideas on the revised edition when taking my graduate quantum me-chanics course at the University of Hawaii during the spring of 1992. Suzukiprovided the initial translation from Japanese of Supplement I as a courseterm paper. Dr. Andy Acker provided me with computer graphic assis-tance. The Department of Physics and Astronomy and particularly theHigh Energy Physics Groupof the University of Hawaii at Manoa providedagain both the facilities and a conducive atmosphere for me to carry outmy editorial task. Finally I wish to express my gratitude to Physics (andsponsoring) Senior Editor, Stuart Johnson, and his Editorial Assistant,Jennifer Duggan, as well as Senior Production Coordinator Amy Willcutt,of Addison-Wesley for their encouragement and optimism that the revisededition will indeed materialize.SanFu TUANHonolulu, Hawaii
8号J.J.Sakurai 1933-1982vi
In MemoriamJun John Sakurai was born in1933 inTokyo and came to the United Statesas a high school student in 1949. He studied at Harvard and at Cornellwhere he received his Ph.D. in 1958. He was then appointed assistantprofessor of Physics at the University of Chicago, and became a fullprofessor in 1964. He stayed at Chicago until 1970 when he moved to theUniversity of California at Los Angeles, where he remained until his death.During his lifetime he wrote 1i9 articles in theoretical physics of elementaryparticles as well as several books and monographs on both quantum andparticle theory.The discipline of theoretical physics has as its principal aim theformulation of theoretical descriptions of the physical world that are at onceconcise and comprehensive. Because nature is subtle and complex,thepursuit of theoretical physics requires bold and enthusiastic ventures to thefrontiers of newly discovered phenomena. This is an area in which Sakuraireigned supreme with his uncanny physical insight and intuition and alsohis ability to explain these phenomena in illuminating physical terms to theunsophisticated. One has but to read his very lucid textbooks on InvariancePrinciples and Elementary Particles and Advanced Quantum Mechanics aswell as his reviews and summer school lectures to appreciate this. Withoutexaggeration I could say that much of what I did understand in particlephysics came from these and from his articles and private tutoring.When Sakurai was still a graduate student, he proposed what is nowknown as the V-A theory of weak interactions, independently of (andsimultaneously with) Richard Feynman, Murray Gcll-Mann, RobcrtMarshak, and George Sudarshan. In 1960 he published in Annals of Physicsa prophetic paper,probably his single most important one. It was concernedwith the first serious attempt to construct a theory of strong interactionsbased on Abelian and non-Abelian (Yang-Mills) gauge invariance. Thisseminal work induced theorists to attempt an understanding of the mecha-nisms of mass generation for gauge (vector)fields, now realized as the Higgsmechanism.Above all it stimulated the search for a realistic unification offorces under the gauge principle, now crowned with success in the cel-ebrated Glashow-Weinberg-Salam unification of weak and electromagneticforces.On the phenomenological side, Sakurai pursued and vigorouslyadvocatedthe vectormesons dominancemodel ofhadrondynamics.Hewasthe first to discuss the mixing of w and meson states. Indeed, he madenumerous important contributions to particle physics phenomenology in avi
viiInMemoriammuch morc general sensc, as his heart was always close to experimentalactivities.I knew Jun John for more than 25 years, and I had the greatestadmiration not only for his immense powers as a theoretical physicist butalso for the warmth and generosity of his spirit. Though a graduate studenthimself at Cornell during 1957-1958, he took tine fron his own pioneeringresearch in K-nucleon dispersion relations to help me (via extensive corre-spondence) with my Ph.D. thesis on the same subject at Berkeley. BothSandip Pakvasa and I were privileged to be associated with one of his lastpapers on weak couplings of heavy quarks, which displayed once more hisinfectious and intuitive style of doing physics. It is of course gratifying to usin retrospect that Jun John counted this paper among the score of hispublished works that he particularly enjoyed.The physics community suffered a great loss at Jun John Sakurai'sdeath. The personal sense of loss is a severe one for me. Hence I amprofoundly thankful for the opportunity to edit and complete his manuscripton Modern Quantum Mechanics for publication. In my faith no greatergift can be given me than an opportunity to show my respect and love forJun John through meaningful service.San Fu Tuan
ContentsiliForewordivPrefaceviiInMemoriam11 FUNDAMENTALCONCEPTS21.1The Stern-Gerlach Experiment101.2Kets, Bras, and Operators171.3Base Kets and Matrix Representations231.4Measurements, Observables, and the Uncertainty Relations361.5Change of Basis411.6Position, Momentum, and Translation511.7Wave Functions in Position and Momentum Space60Problems682QUANTUMDYNAMICS682.1Timc Evolution and the Schrodingcr Equation802.2The Schrodinger Versus the Heisenberg Picture892.3Simple Harmonic Oscillator972.4Schrodinger's Wave Equation2.5109Propagators and Feynman PathIntegrals1232.6Potentials and Gauge Transformations143Problems1523THEORYOFANGULARMOMENTUM3.1152Rotations and Angular Momentum Commutation Relations3.2158Spin1/2 Systems and Finite Rotations3.3168SO(3), sU(2), and Euler Rotations3.4174Density Operators and Pure Versus Mixed Ensembles3.5187Eigenvalues and Eigenstates of Angular Momentum1953.6OrbitalAngularMomentum3.7203Addition of Angular Momenta2173.8Schwinger's Oscillator Model of Angular Momentum2233.9Spin Correlation Measurements and Bel's Inequality2323.10 Tensor Operators242Problems2484 SYMMETRYINOUANTUMMECHANICS2484.1Symmetries, Conservation Laws, and Degeneracies2514.2Discrete Symmetries, Parity, or Space Inversion2614.3Lattice Translation as a Discrete Symmetry2664.4The Time-Reversal Discrete Syimmetry282Problemsix