Lectures on quantum mechanics for mathematics students
发布日期:2009-12-31 浏览次
【内容简介】
This book is based on notes from the course developed and taught for more than 30 years at the Department of Mathematics of Leningrad University. The goal of the course was to present the basics of quantum mechanics and its mathematical content to students in mathematics. This book differs from the majority of other textbooks on the subject in that much more attention is paid to general principles of quantum mechanics. In particular, the authors describe in detail the relation between classical and quantum mechanics. When selecting particular topics, the authors emphasize those that are related to interesting mathematical theories. In particular, the book contains a discussion of problems related to group representation theory and to scattering theory. This book is rather elementary and concise, and it does not require prerequisites beyond the standard undergraduate mathematical curriculum. It is aimed at giving a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.
【目次】 1 The algebra of observables in classical mechanics 1 2 States 6 3 Liouville's theorem, and two pictures of motion in classical mechanics 13 4 Physical bases of quantum mechanics 15 5 A finite-dimensional model of quantum mechanics 27 6 States in quantum mechanics 32 7 Heisenberg uncertainty relations 36 8 Physical meaning of the eigenvalues and eigenvectors of observables 39 9 Two pictures of motion in quantum mechanics. The Schrodinger equation. Stationary states 44 10 Quantum mechanics of real systems. The Heisenberg commutation relations 49 11 Coordinate and momentum representations 54 12 "Eigenfunctions" of the operators Q and P 60 13 The energy, the angular momentum, and other examples of observables 63 14 The interconnection between quantum and classical mechanics. Passage to the limit from quantum mechanics to classical mechanics 69 15 One-dimensional problems of quantum mechanics. A free one-dimensional particle 77 16 The harmonic oscillator 83 17 The problem of the oscillator in the coordinate representation 87 18 Representation of the states of a one-dimensional particle in the sequence space 12 90 19 Representation of the states for a one-dimensional particle in the space D of entire analytic functions 94 20 The general case of one-dimensional motion 95 21 Three-dimensional problems in quantum mechanics. A three-dimensional free particle 103 More...
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