Book contents
- Frontmatter
- Contents
- Editor's Statement
- Foreword
- Preface
- The Logic of Quantum Mechanics
- Part I HILBERT-SPACE QUANTUM MECHANICS
- Chapter 1 Static Description of Quantum Systems
- Chapter 2 States
- Chapter 3 Physical Quantities
- Chapter 4 Spin and Motion
- Chapter 5 Superselection Rules
- Chapter 6 Dynamical Evolution
- Chapter 7 Compound System
- Chapter 8 Elementary Analysis of the Measurement Process
- Chapter 9 Mathematical Structures Emerging from the Hilbert-Space Formulation of Quantum Mechanics
- Part II BASIC STRUCTURES IN THE DESCRIPTION OF QUANTUM SYSTEMS
- Part III RECONSTRUCTION OF HILBERT-SPACE QUANTUM MECHANICS
- Appendix A Trace-Class Operators
- Appendix B The Spectral Theorem
- Appendix C Proofs for Chapter 11
- Subject Index
- Miscellaneous Endmatter
Chapter 6 - Dynamical Evolution
Published online by Cambridge University Press: 05 June 2013
- Frontmatter
- Contents
- Editor's Statement
- Foreword
- Preface
- The Logic of Quantum Mechanics
- Part I HILBERT-SPACE QUANTUM MECHANICS
- Chapter 1 Static Description of Quantum Systems
- Chapter 2 States
- Chapter 3 Physical Quantities
- Chapter 4 Spin and Motion
- Chapter 5 Superselection Rules
- Chapter 6 Dynamical Evolution
- Chapter 7 Compound System
- Chapter 8 Elementary Analysis of the Measurement Process
- Chapter 9 Mathematical Structures Emerging from the Hilbert-Space Formulation of Quantum Mechanics
- Part II BASIC STRUCTURES IN THE DESCRIPTION OF QUANTUM SYSTEMS
- Part III RECONSTRUCTION OF HILBERT-SPACE QUANTUM MECHANICS
- Appendix A Trace-Class Operators
- Appendix B The Spectral Theorem
- Appendix C Proofs for Chapter 11
- Subject Index
- Miscellaneous Endmatter
Summary
The Unitary Dynamical Group in Schrödinger's Picture
Up to now we have been concerned with the description of a physical system at a fixed instant of time. The time evolution of quantum systems constitutes a many-faced, wide issue which, however, is somewhat tangential to the main aim of this volume. We shall touch upon it only briefly, restricting ourselves to the more familiar aspects of the problem.
We assume, to begin with, that the physical system has no superselection rules, so that states and physical quantities correspond one-to-one to density operators and self-adjoint operators, respectively, on the Hilbert space. To describe the dynamical evolution of the system one has to specify the way the representatives of states and physical quantities evolve in, which is fixed in time, since the physical system is supposed to preserve its identity.
There is an old tenet according to which there are two kinds of time evolution: the discontinuous, nondeterministic evolution undergone by the quantum system when a measurement is made on it, and the continuous, deterministic evolution caused by the interaction with external forces or with other quantum systems. The first kind of evolution will be dealt with in Chapter 8, where we shall find it less alarming than is often claimed.
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- The Logic of Quantum Mechanics , pp. 52 - 60Publisher: Cambridge University PressPrint publication year: 1984