Commutation relations, normal ordering, and Stirling numbers. (2015)
- Record Type:
- Book
- Title:
- Commutation relations, normal ordering, and Stirling numbers. (2015)
- Main Title:
- Commutation relations, normal ordering, and Stirling numbers
- Further Information:
- Note: Toufik Mansour, Matthias Schork.
- Authors:
- Mansour, Toufik
Schork, Matthias - Contents:
- Introduction; Set Partitions, Stirling, and Bell Numbers; Commutation Relations and Operator Ordering; Normal Ordering in the Weyl Algebra and Relatives; Content of the Book Basic Tools; Sequences; Solving Recurrence Relations; Generating Functions; Combinatorial Structures; Riordan Arrays and Sheffer Sequences Stirling and Bell Numbers; Definition and Basic Properties of Stirling and Bell Numbers; Further Properties of Bell Numbers; q -Deformed Stirling and Bell Numbers; (p, q )-Deformed Stirling and Bell Numbers Generalizations of Stirling Numbers; Generalized Stirling Numbers as Expansion Coefficients in Operational Relations; Stirling Numbers of Hsu and Shiue: A Grand Unification; Deformations of Stirling Numbers of Hsu and Shiue; Other Generalizations of Stirling Numbers The Weyl Algebra, Quantum Theory, and Normal Ordering ; The Weyl Algebra; Short Introduction to Elementary Quantum Mechanics; Physical Aspects of Normal Ordering Normal Ordering in the Weyl Algebra—Further Aspects ; Normal Ordering in the Weyl Algebra; Wick’s Theorem; The Monomiality Principle; Further Connections to Combinatorial Structures; A Collection of Operator Ordering Schemes; The Multi-Mode Case The q -Deformed Weyl Algebra and the Meromorphic Weyl Algebra ; Remarks on q -Commuting Variables; The q -Deformed Weyl Algebra; The Meromorphic Weyl Algebra; The q -Meromorphic Weyl Algebra A Generalization of the Weyl Algebra ; Definition and Literature; Normal Ordering in Special Ore Extensions;Introduction; Set Partitions, Stirling, and Bell Numbers; Commutation Relations and Operator Ordering; Normal Ordering in the Weyl Algebra and Relatives; Content of the Book Basic Tools; Sequences; Solving Recurrence Relations; Generating Functions; Combinatorial Structures; Riordan Arrays and Sheffer Sequences Stirling and Bell Numbers; Definition and Basic Properties of Stirling and Bell Numbers; Further Properties of Bell Numbers; q -Deformed Stirling and Bell Numbers; (p, q )-Deformed Stirling and Bell Numbers Generalizations of Stirling Numbers; Generalized Stirling Numbers as Expansion Coefficients in Operational Relations; Stirling Numbers of Hsu and Shiue: A Grand Unification; Deformations of Stirling Numbers of Hsu and Shiue; Other Generalizations of Stirling Numbers The Weyl Algebra, Quantum Theory, and Normal Ordering ; The Weyl Algebra; Short Introduction to Elementary Quantum Mechanics; Physical Aspects of Normal Ordering Normal Ordering in the Weyl Algebra—Further Aspects ; Normal Ordering in the Weyl Algebra; Wick’s Theorem; The Monomiality Principle; Further Connections to Combinatorial Structures; A Collection of Operator Ordering Schemes; The Multi-Mode Case The q -Deformed Weyl Algebra and the Meromorphic Weyl Algebra ; Remarks on q -Commuting Variables; The q -Deformed Weyl Algebra; The Meromorphic Weyl Algebra; The q -Meromorphic Weyl Algebra A Generalization of the Weyl Algebra ; Definition and Literature; Normal Ordering in Special Ore Extensions; Basic Observations for the Generalized Weyl Algebra; Aspects of Normal Ordering; Associated Stirling and Bell Numbers The q -Deformed Generalized Weyl Algebra ; Definition and Literature; Basic Observations; Binomial Formula; Associated Stirling and Bell Numbers A Generalization of Touchard Polynomials; Touchard Polynomials of Arbitrary Integer Order; Outlook: Touchard Functions of Real Order; Outlook: ComtetTouchard Functions; Outlook: q -Deformed Generalized Touchard Polynomials Appendices Bibliography Indices Exercises appear at the end of each chapter. … (more)
- Edition:
- 1st
- Publisher Details:
- Boca Raton : Chapman & Hall/CRC
- Publication Date:
- 2015
- Extent:
- 1 online resource, illustrations (black and white)
- Subjects:
- 512.44
Commutative algebra - Languages:
- English
- ISBNs:
- 9781466579897
- Related ISBNs:
- 9781466579880
- Notes:
- Note: Description based on CIP data; item not viewed.
- Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.137344
- Ingest File:
- 02_127.xml