Jj sakurai modern quantum mechanics pdf free download

Professor Roger Newton of Indiana University contributed refinements on lifetime broadening in Stark effect, additional explanations of phase shifts at res- onances, the optical theorem, and on non-normalizable state. Though not a major part of the text, some additions were deemed necessary to take into account developments in quantum mechanics that have become prominent since November 1, To this end, two sup- plements are included at the end of the text. Supplement I is on adiabatic change and geometrical phase popularized by M.

Sudarshan of the University of Texas at Austin. Though non-exponential decays have a long history theoretically, experimental work on transition rates that tests indirectly such decays was done only in Introduction of additional material is of course a subjective matter on the part of the Editor; the readers will evaluate for themselves its appropriateness.

My colleague, Professor Sandip Pakvasa, provided overall guidance and en- couragement to me throughout this process of revision. Preface to the Revised Edition v In addition to the acknowledgments above, my former students Li Ping, Shi Xiaohong, and Yasunaga Suzuki provided the sounding board for ideas on the revised edition when taking my graduate quantum me- chanics course at the University of Hawaii during the spring of Suzuki provided the initial translation from Japanese of Supplement I as a course term paper.

Andy Acker provided me with computer graphic assis- tance. The Department of Physics and Astronomy and particularly the High Energy Physics Group of the University of Hawaii at Manoa provided again both the facilities and a conducive atmosphere for me to carry out my editorial task.

Finally I wish to express my gratitude to Physics and sponsoring 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 revised edition will indeed materialize.

He studied at Harvard and at Cornell, where he received his Ph. He was then appointed assistant professor of Physics at the University of Chicago, and became a full professor in He stayed at Chicago until when he moved to the University of California at Los Angeles, where he remained until his death.

During his lifetime he wrote articles in theoretical physics of elementary particles as well as several books and monographs on both quantum and particle theory. The discipline of theoretical physics has as its principal aim the formulation of theoretical descriptions of the physical world that are at once concise and comprehensive. Because nature is subtle and complex, the pursuit of theoretical physics requires bold and enthusiastic ventures to the frontiers of newly discovered phenomena.

This is an area in which Sakurai reigned supreme with his uncanny physical insight and intuition and also his ability to explain these phenomena in illuminating physical terms to the unsophisticated.

One has but to read his very lucid textbooks on Invariance Principles and Elementary Particles and Advanced Quantum Mechanics as well as his reviews and summer school lectures to appreciate this. Without exaggeration I could say that much of what I did understand in particle physics came from these and from his articles and private tutoring. When Sakurai was still a graduate student, he proposed what is now known as the V-A theory of weak interactions, independently of and simultaneously with Richard Feynman, Murray Gell-Mann, Robert Marshak, and George Sudarshan.

In he published in Annals of Physics a prophetic paper, probably his single most important one. It was concerned with the first serious attempt to construct a theory of strong interactions based on Abelian and non-Abelian Yang-Mills gauge invariance. This seminal work induced theorists to attempt an understanding of the mecha- nisms of mass generation for gauge vector fields, now realized as the Higgs mechanism.

Above all it stimulated the search for a realistic unification of forces under the gauge principle, now crowned with success in the cel- ebrated Glashow-Weinberg-Salam unification of weak and electromagnetic forces. On the phenomenological side, Sakurai pursued and vigorously advocated the vector mesons dominance model of hadron dynamics.

Though a graduate student himself at Cornell during , he took time from his own pioneering research in K-nucleon dispersion relations to help me via extensive corre- spondence with my Ph. Both Sandip Pakvasa and I were privileged to be associated with one of his last papers on weak couplings of heavy quarks, which displayed once more his infectious and intuitive style of doing physics.

It is of course gratifying to us in retrospect that Jun John counted this paper among the score of his published works that he particularly enjoyed.

The personal sense of loss is a severe one for me. Hence J am profoundly thankful for the opportunity to edit and complete his manuscript on Modern Quantum Mechanics for publication. In my faith no greater gift can be given me than an opportunity to show my respect and love for Jun John through meaningful service.

Kets, Bras, and Operators 1. Change of Basis 1. Not only did we witness severe limitations in the validity of classical physics, but we found the alternative theory that replaced the classical physical theories to be far richer in scope and far richer in its range of applicability.

However, we do not follow the historical approach in this book. Instead, we start with an example that illustrates, perhaps more than any other example, the inadequacy of classical concepts in a fundamental way. Stern in and carried out in Frankfurt by him in collaboration with W. Gerlach in This experiment illustrates in a dramatic manner the necessity for a radical departure from the concepts of classical mechanics.

In the subsequent sections the basic for- malism of quantum mechanics is presented in a somewhat axiomatic manner but always with the example of the Stern-Gerlach experiment in the back of our minds.

In a certain sense, a two-state system of the Stern-Gerlach type is the least classical, most quantum-mechanical system. A solid understand- ing of problems involving two-state systems will turn out to be rewarding to any serious student of quantum mechanics.

It is for this reason that we refer repeatedly to two-state problems throughout this book. Description of the Experiment We now present a brief discussion of the Stern-Gerlach experiment, which is discussed in almost any book on modern physics. First, silver Ag atoms are heated in an oven.

The oven has a small hole through which some of the silver atoms escape. As shown in Figure 1. We must now work out the effect of the magnetic field on the silver atoms. For our purpose the following oversimplified model of the silver atom suffices. The silver atom is made up of a nucleus and 47 electrons, where 46 out of the 47 electrons can be visualized as forming a spherically symmetrical electron cloud with no net angular momentum.

If we ignore the nuclear spin, which is irrelevant to our discussion, we see that the atom as a whole does have an angular momentum, which is due solely to the spin— intrinsic as opposed to orbital—angular momentum of the single 47th Ss electron. The Stern-Gerlach experiment. The beam is then expected to get split according to the values of.. The atoms in the oven are randomly oriented; there is no preferred direction for the orientation of p. If the electron were like a classical spinning object, we would expect all values of jz, to be realized between p and — p.

This would lead us to expect a continuous bundle of beams coming out of the SG apparatus, as shown in Figure 1. Beams from the SG apparatus; a is expected from classical physics, while b is actually observed, experimentally observe is more like the situation in Figure 1. Of course, there is nothing sacred about the up-down direction or the z-axis. We could just as well have applied an inhomogeneous field in a horizontal direction, say in the x-direction, with the beam proceeding in the y-direction.

By this we mean that the atomic beam goes through two or more SG apparatuses in sequence. The first arrangement we consider is relatively straightforward. We subject the beam coming out of the oven to the arrangement shown in Figure 1. The Stern-Gerlach Experiment 5 Szt comp. Sit beam. Sequential Stern-Gerlach experiments. This is perhaps not so surprising; after all if the atom spins are up, they are expected to remain so, short of any external field that rotates the spins between the first and the second SG2 apparatuses.

A little more interesting is the arrangement shown in Figure 1. How can we explain this? It turns out that such a picture runs into difficulty, as will be shown below. We now consider a third step, the arrangement shown in Figure 1. This time we add to the arrangement of Figure 1. How is it possible that the S, — component which, we thought, we eliminated earlier reappears?

This example is often used to illustrate that in quantum mechanics we cannot determine both S, and S, simultaneously. By observing how fast the object is spinning in which direction we can determine w,, w,, and «, simultaneously.

The moment of inertia J is computable if we know the mass density and the geometric shape of the spinning top, so there is no difficulty in specifying both L, and L, in this classical situation. It is to be clearly understood that the limitation we have encountered in determining S, and S, is not due to the incompetence of the experi- mentalist. By improving the experimental techniques we cannot make the S. The peculiarities of quantum mechanics are imposed upon us by the experiment itself.

The limitation is, in fact, inherent in microscopic phenomena. Analogy with Polarization of Light Because this situation looks so novel, some analogy with a familiar classical situation may be helpful here. To this end we now digress to consider the polarization of light waves. Consider a monochromatic light wave propagating in the z-direction. We call a filter that selects only beams polarized in the x-direction an x-filter. Light beams subjected to Polaroid filters.

This time, there is a light beam coming out of the y-filter despite the fact that right after the beam went through the x-filter it did not have any polarization component in the y-direction. Notice that this situation is quite analogous to the situation that we encountered earlier with the SG arrangement of Figure 1. Using Figure 1. And finally, the third Polaroid selects the y-polarized component. Applying correspondence 1. So we may conjecture 1.

Later we will show how to obtain these expressions using the general formalism of quantum mechanics. Thus the unblocked component coming out of the second SG apparatus of Figure 1.

It is for this reason that two components emerge from the third SG2 apparatus. An analogy with polarized light again rescues us here. This time we consider a circularly polarized beam of light, which can be obtained by letting a linearly polarized light pass through a quarter-wave plate. When we pass such a circularly polarized light through an x-filter or a y-filter, we again obtain either an x-polarized beam or a y-polarized beam of equal intensity.

Mathematically, how do we represent a circularly polarized light? Applying this analogy to 1. We thus see that the two-dimen- sional vector space needed to describe the spin states of silver atoms must be a complex vector space; an arbitrary vector in the vector space is written as a linear combination of the base vectors S. The fact that the necessity of complex numbers is already apparent in such an elementary example is rather remarkable. The reader must have noted by this time that we have deliberately avoided talking about photons.

Genres: Mathematics. The approach emphasizes states, operators, eigenvalues, and representations from the start. This approach also helps the reader gain an appreciation of purely quantum-mechanical phenomena, for example the magnetic moment and spin of an electron, that have no classical analogue.

The intended audience is the same as for earlier editions, that is, students having taken upper level undergraduate coursework in quantum physics, classical mechanics and electromagnetism, multivariable calculus, and ordinary and partial differential equations. This volume contained a lot of new material, including an eighth chapter, and was published in I was therefore pleased to be asked to take on the Second Edition.

Groups are also introduced here, with further exposition in Chapter Four. The Third Edition keeps the same ordering of the eight chapters. The Third Edition addresses all of the errors. It also addresses most of the comments, having to give up on some only for lack of time. There are three new sections of new material. Despite its increasing use in condensed matter physics, I found no treatments of density functional theory in any quantum mechanics textbook.

So, I added Section 7. The Second Edition treated spontaneous emission only as an end-of-chapter problem, but Section 5. Instructors may elect to pick and choose from topics in the book, and not necessarily in the order of presentation.