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Quantum Dynamics for Classical Systems : With Applications of the Number Operator.

Author: F Bagarello
Publisher: New York : Wiley, 2012.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
With a focus on the relationship between quantum mechanics and social science, this book introduces the main ideas of number operators while avoiding excessive technicalities that aren't necessary in understanding the various mathematical applications. It discusses the use of mathematical tools related to quantum mechanics and features applications in finance, biology, and social science; systematically shows how to  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: F Bagarello
ISBN: 9781118400593 1118400593
OCLC Number: 815650925
Description: 1 online resource (246 pages)
Contents: QUANTUM DYNAMICS FOR CLASSICAL SYSTEMS; CONTENTS; PREFACE; ACKNOWLEDGMENTS; 1 WHY A QUANTUM TOOL IN CLASSICAL CONTEXTS?; 1.1 A First View of (Anti- )Commutation Rules; 1.2 Our Point of View; 1.3 Do Not Worry About Heisenberg!; 1.4 Other Appearances of Quantum Mechanics in Classical Problems; 1.5 Organization of the Book; 2 SOME PRELIMINARIES; 2.1 The Bosonic Number Operator; 2.2 The Fermionic Number Operator; 2.3 Dynamics for a Quantum System; 2.3.1 Schrödinger Representation; 2.3.2 Heisenberg Representation; 2.3.3 Interaction Representation; 2.4 Heisenberg Uncertainty Principle. 2.5 Some Perturbation Schemes in Quantum Mechanics2.5.1 A Time-Dependent Point of View; 2.5.2 Feynman Graphs; 2.5.3 Dyson's Perturbation Theory; 2.5.4 The Stochastic Limit; 2.6 Few Words on States; 2.7 Getting an Exponential Law from a Hamiltonian; 2.7.1 Non-Self-Adjoint Hamiltonians for Damping; 2.8 Green's Function; I SYSTEMS WITH FEW ACTORS; 3 LOVE AFFAIRS; 3.1 Introduction and Preliminaries; 3.2 The First Model; 3.2.1 Numerical Results for M> 1; 3.3 A Love Triangle; 3.3.1 Another Generalization; 3.4 Damped Love Affairs; 3.4.1 Some Plots; 3.5 Comparison with Other Strategies. 4 MIGRATION AND INTERACTION BETWEEN SPECIES4.1 Introduction and Preliminaries; 4.2 A First Model; 4.3 A Spatial Model; 4.3.1 A Simple Case: Equal Coefficients; 4.3.2 Back to the General Case: Migration; 4.4 The Role of a Reservoir; 4.5 Competition Between Populations; 4.6 Further Comments; 5 LEVELS OF WELFARE: THE ROLE OF RESERVOIRS; 5.1 The Model; 5.2 The Small l Regime; 5.2.1 The Sub-Closed System; 5.2.2 And Now, the Reservoirs!; 5.3 Back to S; 5.3.1 What If M = 2?; 5.4 Final Comments; 6 AN INTERLUDE: WRITING THE HAMILTONIAN; 6.1 Closed Systems; 6.2 Open Systems; 6.3 Generalizations. II SYSTEMS WITH MANY ACTORS7 A FIRST LOOK AT STOCK MARKETS; 7.1 An Introductory Model; 8 ALL-IN-ONE MODELS; 8.1 The Genesis of the Model; 8.1.1 The Effective Hamiltonian; 8.2 A Two-Traders Model; 8.2.1 An Interlude: the Definition of cP; 8.2.2 Back to the Model; 8.3 Many Traders; 8.3.1 The Stochastic Limit of the Model; 8.3.2 The FPL Approximation; 9 MODELS WITH AN EXTERNAL FIELD; 9.1 The Mixed Model; 9.1.1 Interpretation of the Parameters; 9.2 A Time-Dependent Point of View; 9.2.1 First-Order Corrections; 9.2.2 Second-Order Corrections; 9.2.3 Feynman Graphs; 9.3 Final Considerations. 10 CONCLUSIONS10.1 Other Possible Number Operators; 10.1.1 Pauli Matrices; 10.1.2 Pseudobosons; 10.1.3 Nonlinear Pseudobosons; 10.1.4 Algebra for an M + 1 Level System; 10.2 What Else?; BIBLIOGRAPHY; INDEX.

Abstract:

With a focus on the relationship between quantum mechanics and social science, this book introduces the main ideas of number operators while avoiding excessive technicalities that aren't necessary in understanding the various mathematical applications. It discusses the use of mathematical tools related to quantum mechanics and features applications in finance, biology, and social science; systematically shows how to use creation and annihilation operators for classical problems; and addresses the recent increase in research and literature on the many applications of quantum tools in applied ma.

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