Lectures on quantum mechanics

Abstract

In his book “Lectures onQuantumMechanics”, StevenWeinberg presents thematerial he has covered in a one-year course on quantum mechanics. In his preface, he states that each section of his book roughly corresponds to a seventy-five-minute lecture, indicating that the book is a near representation of the course as he has given it. After having reviewed this book, I am certain that the students had a very good course. The first two chapters begin with a review of the history of the experimental and theoretical problems with classical physics, the subsequent introduction of the uncertainty principle, the Schrodinger equation, the probabilistic interpretation of the wave function, the solution of the Schrodinger equation for the Coulomb potential with a discussion of the energy levels and wave functions for the hydrogen atom. In Chapter 3, Weinberg formulates the general principles of quantum mechanics, associatingobservable physical quantitieswithHermitianoperatorswhose eigenvalues and eigenvectors determine the expectation values of the corresponding observables. Symmetries are associated with unitary operators transforming states, and the effect of an infinitesimal symmetry transformation on any observable is determined by the commutator of the symmetry generator with the operator associated with the observable, a fact made use of extensively throughout these lectures. Weinberg is sufficiently uneasy about the use of a quantum mechanical state vector solely as an algorithm for calculating probabilities that he devotes the longest section in the book to a discussion of various attempts to “derive” the Born rule within the framework of quantum mechanics, concluding that “today there is no interpretation of quantum mechanics that does not have serious flaws.” In Chapter 4, Weinberg presents a lucid and thorough treatment of space-time symmetries and internal symmetries, both continuous and discrete, and of symmetry