Foundations of quantum mechanics

Author(s)

• Ludwig, Günther

Bibliographic Information

Foundations of quantum mechanics

G. Ludwig ; translated by Carl A. Hein

（Texts and monographs in physics）

Springer-Verlag, c1983-c1985

• v. 1 : us
• v. 1 : gw
• v. 2 : us
• v. 2 : gw

Other Title

Die Grundlagen der Quantenmechanik

Note

Translation of: Die Grundlagen der Quantenmechanik

Includes bibliographies and indexes

Description and Table of Contents

Volume

v. 1 : gw ISBN 9783540116837

Table of Contents

• I The Problem: An Axiomatic Basis for Quantum Mechanics.- 1 The Axiomatic Formulation of a Physical Theory.- 2 The Fundamental Domain for Quantum Mechanics.- 3 The Measurement Problem.- II Microsystems, Preparation, and Registration Procedures.- 1 The Concept of a Physical Object.- 2 Selection Procedures.- 3 Statistical Selection Procedures.- 4 Physical Systems.- 4.1 Preparation Procedures.- 4.2 Registration Procedures.- 4.3 The Dependence of Registration upon Preparation.- 4.4 The Concept of a Physical System.- 4.5 The Structure of Probability Fields for Physical Systems.- III Ensembles and Effects.- 1 Combinations of Preparation and Registration Methods.- 2 Mixtures and Decompositions of Ensembles and Effects.- 3 General Laws: Preparation and Registration of Microsystems.- 4 Properties and Pseudoproperties.- 4.1 Properties and Physical Objects.- 4.2 Pseudoproperties.- 5 Ensembles and Effects in Quantum Mechanics.- 6 Decision Effects and Faces of K.- IV Coexistent Effects and Coexistent Decompositions.- 1 Coexistent Effects and Observables.- 1.1 Coexistent Registrations.- 1.2 Coexistent Effects.- 1.3 Commensurable Decision Effects.- 1.4 Observables.- 2 Structures in the Class of Observables.- 2.1 The Spaces ?(?) and ?'(?).- 2.2 Mixture Morphisms Corresponding to an Observable.- 2.3 The Kernel of an Observable
• Mixture of Effects for an Observable.- 2.4 Mixtures and Decompositions of Observables.- 2.5 Measurement Scales for Observables.- 3 Coexistent and Complementary Observables.- 4 Realizations of Observables.- 5 Coexistent Decompositions of Ensembles.- 6 Complementary Decompositions of Ensembles.- 7 Realizations of Decompositions.- 8 Objective Properties and Pseudoproperties of Microsystems.- 8.1 Objective Properties of Microsystems and Superselection Rules.- 8.2 Pseudoproperties of Microsystems.- 8.3 Logic of Decision Effects?.- V Transformations of Registration and Preparation Procedures. Transformations of Effects and Ensembles.- 1 Morphisms for Selection Procedures.- 2 Morphisms of Statistical Selection Procedures.- 3 Morphisms of Preparation and Registration Procedures.- 4 Morphisms of Ensembles and Effects.- 4.1 Morphisms of Ensembles.- 4.2 Morphisms of Effects.- 4.3 Coexistent Operations and Coexistent Effects Morphisms.- 5 Isomorphisms and Automorphisms of Ensembles and Effects.- VI Representation of Groups by Means of Effect Automorphisms and Mixture Automorphisms.- 1 Homomorphic Maps of a Group in the Group of ?-continuous Effect Automorphisms.- 1.1 Generation of a Representation of in by Means of a Representation of by r-Automorphisms.- 1.2 Some General Properties of a Representation of in .- 1.3 Topologies on the Group .- 1.4 The Representation of in Phase Space ?.- 2 The -invariant Structure Corresponding to a Group Representation.- 3 Properties of Representations of which are Dependent on the Special Structure of (?) in Quantum Mechanics.- 3.1 The Topological Structure of the Group (?).- 3.2 The Topological Properties of a Representation of .- 3.3 Unitary and Anti-unitary Representations Up to a Factor.- VII The Galileo Group.- 1 The Galileo Group as a Set of Transformations of Registration Procedures Relative to Preparation Procedures.- 2 Irreducible Representations of the Galileo Group and Their Physical Meaning.- 3 Irreducible Representations of the Rotation Group.- 4 Position and Momentum Observables.- 5 Energy and Angular Momentum Observables.- 6 Time Observable?.- 7 Spatial Reflections (Parity Transformations).- 8 The Problem of the Space for Elementary Systems.- 9 The Problem of Differentiability.- VIII Composite Systems.- 1 Registrations and Effects of the Inner Structure.- 2 Composite Systems Consisting of Two Different Elementary Systems.- 3 Composite Systems Consisting of Two Identical Elementary Systems.- 4 Composite Systems Consisting of Electrons and Atomic Nuclei.- 5 The Hamiltonian Operator.- 6 Microsystems in External Fields.- 7 Criticism of the Description of Interaction in Quantum Mechanics and the Problem of the Space .- Appendix I.- Summary of Lattice Theory.- 1 Definition of a Lattice.- 2 Orthomodularity.- 3 Boolean Rings.- 4 Set Lattices.- Appendix II.- Remarks about Topological and Uniform Structures.- 1 Topological Spaces.- 2 Uniform Spaces.- 3 Baire Spaces.- 4 Connectedness.- Appendix III.- Banach Spaces.- 1 Linear Vector Spaces.- 2 Normed Vector Spaces and Banach Spaces.- 3 The Dual Space for a Banach Space.- 4 Weak Topologies.- 5 Linear Maps of Banach Spaces.- 6 Ordered Vector Spaces.- Appendix IV.- Operators in Hubert Space.- 1 The Hubert Space Structure Type.- 2 Orthogonal Systems and Closed Subspaces.- 3 The Banach Space of Bounded Operators.- 4 Bounded Linear Forms.- 6 Projection Operators.- 7 Isometric and Unitary Operators.- 8 Spectral Representation of Self-adjoint and Unitary Operators.- 9 The Spectrum of Compact Self-adjoint Operators.- 10 Spectral Representation of Unbounded Self-adjoint Operators.- 11 The Trace as a Bilinear Form.- 12 Gleason's Theorem.- 13 Isomorphisms and Anti-isomorphisms.- 14 Products of Hubert Spaces.- References.- List of Frequently Used Symbols.- List of Axioms.

Volume

v. 2 : gw ISBN 9783540130093

Description

In this second volume on the Foundations of Quantum Mechanics we shall show how it is possible, using the methodology presented in Volume I, to deduce some of the most important applications of quantum mechanics. These deductions are concerned with the structures of the micro systems rather than the technical details of the construction of preparation and registration devices. Accordingly, the only new axioms (relative to Volume I) which are introduced are concerned with the relationship between ensemble operators W, effect operators F, and certain construction principles of the preparation and registration devices. The applications described here are concerned with the measurement of atomic and molecular structure and of collision experiments. An additional and essential step towards a theoretical description of the preparation and registration procedures is carried out in Chapter XVII. Here we demonstrate how microscopic collision processes (that is, processes which can be described by quantum mechanics) can be used to obtain novel preparation and registration procedures if we take for granted the knowledge of only a few macroscopic preparation and registration procedures. By clever use of collision processes we are often able to obtain very precise results for the operators Wand F which describe the total procedures from a very imprecise knowledge of the macroscopic parts of the preparation and regis- tration processes. In this regard experimental physicists have done brilliant work. In this sense Chapter XVII represents a general theoretical foundation for the procedures used by experimental physicists.

Table of Contents

(Volume II).- IX Representation of Hilbert Spaces by Function Spaces.- 1 Maximal Decision Observables.- 2 Representation of ? as ?2(Sp(A), ?) where Sp(A) is the Spectrum of a Scale Observable A.- 3 Improper Scalar and Vector Functions Defined on Sp(A).- 4 Transformation of One Representation into Another.- 5 Position and Momentum Representation.- 6 Degenerate Spectra.- X Equations of Motion.- 1 The Heisenberg Picture.- 2 The Schrodinger Picture.- 3 The Interaction Picture.- 4 Time Reversal Transformations.- XI The Spectrum of One-Electron Systems.- 1 The Effect of the Emission of a Photon.- 2 Ensembles Consisting of Bound States.- 3 The Spectrum of Hydrogen-like Atoms.- 4 The Eigenfunctions for the Discrete Spectrum.- 5 The Continuous Spectrum.- 6 Perturbation Theory.- 7 Perturbation Computations and Symmetry.- 8 The Spectrum of Alkali Atoms.- 9 Electron Spin.- 10 Addition of Angular Momentum.- 11 Fine Structure of Hydrogen and Alkali Metals.- XII Spectrum of Two-Electron Systems.- 1 The Hilbert Space and the Hamiltonian Operator for the Internal Motion of Atoms with n Electrons.- 2 The Spectrum of Two-Electron Atoms.- 3 Ritz Variational Principle.- 4 The Fine Structure of the Helium Spectrum.- XIII Selection Rules and the Intensity of Spectral Lines.- 1 Intensity of Spectral Lines.- 2 Representation Theory and Matrix Elements.- 3 Selection Rules for One-Electron Spectra.- 4 Selection Rules for the Helium Spectrum.- XIV Spectra of Many-Electron Systems.- 1 Energy Terms in the Absence of Spin.- 2 Fine Structure Splitting of Spectral Lines.- 3 Structure Principles.- 4 The Periodic System of the Elements.- 5 Selection and Intensity Rules.- 6 Zeeman Effect.- 7 f Electron Problems and the Symmetric Group.- 8 The Characters for the Representations of Sf and Un.- 9 Perturbation Computations.- XV Molecular Spectra and the Chemical Bond.- 1 The Hamiltonian Operator for a Molecule.- 2 The Form of the Eigenfunctions.- 3 The Ionized Hydrogen Molecule.- 4 Structure Principles for Molecular Energy Levels.- 5 Formation of a Molecule from Two Atoms.- 6 The Hydrogen Molecule.- 7 The Chemical Bond.- 8 Spectra of Diatomic Molecules.- 9 The Effect of Electron Spin on Molecular Energy Levels.- XVI Scattering Theory.- 1 General Properties of Ensembles Used in Scattering Experiments.- 2 General Properties of Effects Used in Scattering Experiments.- 3 Separation of Center of Mass Motion.- 4 Wave Operators and the Scattering Operator.- 4.1 Definition of the Wave Operators.- 4.2 Some General Properties of Wave Operators.- 4.3 Wave Operators and the Spectral Representation of the Hamiltonian Operators.- 4.4 The S Operator.- 4.5 A Sufficient Condition for the Existence of Normal Wave Operators.- 4.6 The Existence of Complete Wave Operators.- 4.7 Stationary Scattering Theory.- 4.8 Scattering of a Pair of Identical Elementary Systems.- 4.9 Multiple-Channel Scattering Theory.- 5 Examples of Wave Operators and Scattering Operators.- 5.1 Scattering of an Elementary System of Spin $$ \frac{1}{2} $$ by an Elementary System of Spin 0.- 5.2 The Born Approximation.- 5.3 Scattering of an Electron by a Hydrogen Atom.- 6 Examples of Registrations in Scattering Experiments.- 6.1 The Effect of the "Impact"(Volume II).- IX Representation of Hilbert Spaces by Function Spaces.- 1 Maximal Decision Observables.- 2 Representation of ? as ?2(Sp(A), ?) where Sp(A) is the Spectrum of a Scale Observable A.- 3 Improper Scalar and Vector Functions Defined on Sp(A).- 4 Transformation of One Representation into Another.- 5 Position and Momentum Representation.- 6 Degenerate Spectra.- X Equations of Motion.- 1 The Heisenberg Picture.- 2 The Schrodinger Picture.- 3 The Interaction Picture.- 4 Time Reversal Transformations.- XI The Spectrum of One-Electron Systems.- 1 The Effect of the Emission of a Photon.- 2 Ensembles Consisting of Bound States.- 3 The Spectrum of Hydrogen-like Atoms.- 4 The Eigenfunctions for the Discrete Spectrum.- 5 The Continuous Spectrum.- 6 Perturbation Theory.- 7 Perturbation Computations and Symmetry.- 8 The Spectrum of Alkali Atoms.- 9 Electron Spin.- 10 Addition of Angular Momentum.- 11 Fine Structure of Hydrogen and Alkali Metals.- XII Spectrum of Two-Electron Systems.- 1 The Hilbert Space and the Hamiltonian Operator for the Internal Motion of Atoms with n Electrons.- 2 The Spectrum of Two-Electron Atoms.- 3 Ritz Variational Principle.- 4 The Fine Structure of the Helium Spectrum.- XIII Selection Rules and the Intensity of Spectral Lines.- 1 Intensity of Spectral Lines.- 2 Representation Theory and Matrix Elements.- 3 Selection Rules for One-Electron Spectra.- 4 Selection Rules for the Helium Spectrum.- XIV Spectra of Many-Electron Systems.- 1 Energy Terms in the Absence of Spin.- 2 Fine Structure Splitting of Spectral Lines.- 3 Structure Principles.- 4 The Periodic System of the Elements.- 5 Selection and Intensity Rules.- 6 Zeeman Effect.- 7 f Electron Problems and the Symmetric Group.- 8 The Characters for the Representations of Sf and Un.- 9 Perturbation Computations.- XV Molecular Spectra and the Chemical Bond.- 1 The Hamiltonian Operator for a Molecule.- 2 The Form of the Eigenfunctions.- 3 The Ionized Hydrogen Molecule.- 4 Structure Principles for Molecular Energy Levels.- 5 Formation of a Molecule from Two Atoms.- 6 The Hydrogen Molecule.- 7 The Chemical Bond.- 8 Spectra of Diatomic Molecules.- 9 The Effect of Electron Spin on Molecular Energy Levels.- XVI Scattering Theory.- 1 General Properties of Ensembles Used in Scattering Experiments.- 2 General Properties of Effects Used in Scattering Experiments.- 3 Separation of Center of Mass Motion.- 4 Wave Operators and the Scattering Operator.- 4.1 Definition of the Wave Operators.- 4.2 Some General Properties of Wave Operators.- 4.3 Wave Operators and the Spectral Representation of the Hamiltonian Operators.- 4.4 The S Operator.- 4.5 A Sufficient Condition for the Existence of Normal Wave Operators.- 4.6 The Existence of Complete Wave Operators.- 4.7 Stationary Scattering Theory.- 4.8 Scattering of a Pair of Identical Elementary Systems.- 4.9 Multiple-Channel Scattering Theory.- 5 Examples of Wave Operators and Scattering Operators.- 5.1 Scattering of an Elementary System of Spin $$ \frac{1}{2} $$ by an Elementary System of Spin 0.- 5.2 The Born Approximation.- 5.3 Scattering of an Electron by a Hydrogen Atom.- 6 Examples of Registrations in Scattering Experiments.- 6.1 The Effect of the "Impact" of a Microsystem on a Surface.- 6.2 Counting Microsystems Scattered into a Solid Angle.- 6.3 The Scattering Cross Section.- 7 Survey of Other Problems in Scattering Theory.- XVII The Measurement Process and the Preparation Process.- 1 The Problem of Consistency.- 2 Measurement Scattering Processes.- 2.1 Measurement with a Microscope.- 2.2 Measurement Scattering Morphisms.- 2.3 Properties of Measurement Scattering Morphisms.- 3 Measurement Transformations.- 3.1 Measurement Transformation Morphisms.- 3.2 Properties of Measurement Transformation Morphisms.- 4 Transpreparations.- 4.1 Reduction of a Preparation Procedure by Means of a Registration Procedure.- 4.2 Transpreparation by Means of Scattering.- 4.3 Collapse of Wave Packets?.- 4.4 The Einstein-Podolski-Rosen Paradox.- 5 Measurements of the First Kind.- 6 The Physical Importance of Scattering Processes Used for Registration and Preparation.- 6.1 Sequences of Measurement Scatterings and Measurement Transformations.- 6.2 Physical Importance of Measurement Scattering and Measurement Transformations.- 6.3 Chains of Transpreparations.- 6.4 The Importance of Transpreparators for the Preparation Process.- 6.5 Unstable States.- 7 Complex Preparation and Registration Processes.- XVIII Quantum Mechanics, Macrophysics and Physical World Views.- 1 Universality of Quantum Mechanics?.- 2 Macroscopic Systems.- 3 Compatibility of the Measurement Process with Preparation and Registration Procedures.- 4 "Point in Time" of Measurement in Quantum Mechanics?.- 5 Relationships Between Different Theories and Quantum Mechanics.- 6 Quantum Mechanics and Cosmology.- 7 Quantum Mechanics and Physical World Views.- Appendix V Groups and Their Representations.- 1 Groups.- 2 Cosets and Invariant Subgroups.- 3 Isomorphisms and Homomorphisms.- 4 Isomorphism Theorem.- 5 Direct Products.- 6 Representations of Groups.- 7 The Irreducible Representations of a Finite Group.- 8 Orthogonality Relations for the Elements of Irreducible Representation Matrices.- 9 Representations of the Symmetric Group.- 10 Topological Groups.- 10.1 The Species of Structure: Topological Group.- 10.2 Uniform Structures of Groups.- 10.3 Lie Groups.- 10.4 Representations of Topological Groups.- 10.5 Group Rings of Compact Lie Groups.- 10.6 Representations in Hilbert Space.- 10.7 Representations up to a Factor.- References.

by "Nielsen BookData"

Details

• NCID: BA01213419
• ISBN:
  • 0387116834
  • 3540116834
  • 0387130098
  • 3540130098
• LCCN: 82010437
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: New York
• Pages/Volumes: 2 v.
• Size: 25 cm
• Classification:
  • LCC : QC174.12
  • DC19 : 530.1/2
• Subject Headings:
  • LCSH : Quantum theory
• Parent Bibliography ID:
  • BA00216852