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 1 - Static Description of Quantum Systems
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 Hilbert-Space Description
By the static description of a physical system we mean the rules that assign specified mathematical objects to the states and to the physical quantities of the system, and the prescriptions for calculating the probability distribution of the possible values of every physical quantity when the state of the system is given.
In the usual Hilbert-space formulation of quantum mechanics, to each physical system is attached a separable Hilbert space (generally infinite-dimensional) over the complex field. To every physical quantity is associated a linear, self-adjoint, not necessarily bounded operator on. If one deals with a strictly quantum system, then the converse is also generally assumed: every self-adjoint operator on represents some physical quan- tity. The restriction “strictly quantum” is necessary: if the system retains some nonquantum (i.e. classical) feature, so that it requires the algorithm of so-called “superselection rules” (see Chapter 5), then there are self-adjoint operators on that do not represent physical quantities. It should also be stressed that even in the strictly quantum case, most of the self-adjoint operators actually do not represent “interesting” physical quantities: only a few of them represent physical quantities that are useful and meaningful for the description of the physical system (e.g., energy, momentum, position, angular momentum). Therefore, by asserting that every self-adjoint operator on corresponds to some physical quantity we mean there is no a priori impossibility of devising such a correspondence, but we do not claim that this correspondence is present in the real work of experimental physics.
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- The Logic of Quantum Mechanics , pp. 3 - 5Publisher: Cambridge University PressPrint publication year: 1984