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

✍ Scribed by Fabio Bagarello(auth.)

• Year: 2012
• Tongue: English
• Leaves: 234
• Category: Library

✦ Synopsis

Introduces number operators with a focus on the relationship between quantum mechanics and social science

Mathematics is increasingly applied to classical problems in finance, biology, economics, and elsewhere. Quantum Dynamics for Classical Systems describes how quantum tools?the number operator in particular?can be used to create dynamical systems in which the variables are operator-valued functions and whose results explain the presented model. The book presents mathematical results and their applications to concrete systems and discusses the methods used, results obtained, and techniques developed for the proofs of the results.

The central ideas of number operators are illuminated while avoiding excessive technicalities that are unnecessary for understanding and learning the various mathematical applications. The presented dynamical systems address a variety of contexts and offer clear analyses and explanations of concluded results. Additional features in Quantum Dynamics for Classical Systems include:

• Applications across diverse fields including stock markets and population migration as well as a unique quantum perspective on these classes of models
• Illustrations of the use of creation and annihilation operators for classical problems
• Examples of the recent increase in research and literature on the many applications of quantum tools in applied mathematics
• Clarification on numerous misunderstandings and misnomers while shedding light on new approaches in the field

Quantum Dynamics for Classical Systems is an ideal reference for researchers, professionals, and academics in applied mathematics, economics, physics, biology, and sociology. The book is also excellent for courses in dynamical systems, quantum mechanics, and mathematical models.

Content:
Chapter 1 Why a Quantum Tool in Classical Contexts? (pages 1–9):
Chapter 2 Some Preliminaries (pages 11–46):
Chapter 3 Love Affairs (pages 47–80):
Chapter 4 Migration and Interaction Between Species (pages 81–107):
Chapter 5 Levels of Welfare: The Role of Reservoirs (pages 109–128):
Chapter 6 An Interlude: Writing the Hamiltonian (pages 129–137):
Chapter 7 A First Look at Stock Markets (pages 139–150):
Chapter 8 All?in?One Models (pages 151–185):
Chapter 9 Models with an External Field (pages 187–210):
Chapter 10 Conclusions (pages 211–218):