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Group Theory And Quantum Mechanics by Michael Tinkham
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1Relationships Between Quantum And Classical Mechanics Using The Representation Theory Of The Heisenberg Group
By Alastair Brodlie
This thesis is concerned with the representation theory of the Heisenberg group and its applications to both classical and quantum mechanics. We continue the development of $p$-mechanics which is a consistent physical theory capable of describing both classical and quantum mechanics simultaneously. $p$-Mechanics starts from the observation that the one dimensional representations of the Heisenberg group play the same role in classical mechanics which the infinite dimensional representations play in quantum mechanics. In this thesis we introduce the idea of states to $p$-mechanics. $p$-Mechanical states come in two forms: elements of a Hilbert space and integration kernels. In developing $p$-mechanical states we show that quantum probability amplitudes can be obtained using solely functions/distributions on the Heisenberg group. This theory is applied to the examples of the forced, harmonic and coupled oscillators. In doing so we show that both the quantum and classical dynamics of these systems can be derived from the same source. Also using $p$-mechanics we simplify some of the current quantum mechanical calculations. We also analyse the role of both linear and non-linear canonical transformations in $p$-mechanics. We enhance a method derived by Moshinsky for studying the passage of canonical transformations from classical to quantum mechanics. The Kepler/Coulomb problem is also examined in the $p$-mechanical context. In analysing this problem we show some limitations of the current $p$-mechanical approach. We then use Klauder's coherent states to generate a Hilbert space which is particularly useful for the Kepler/Coulomb problem.
“Relationships Between Quantum And Classical Mechanics Using The Representation Theory Of The Heisenberg Group” Metadata:
- Title: ➤ Relationships Between Quantum And Classical Mechanics Using The Representation Theory Of The Heisenberg Group
- Author: Alastair Brodlie
- Language: English
Edition Identifiers:
- Internet Archive ID: arxiv-quant-ph0412015
Downloads Information:
The book is available for download in "texts" format, the size of the file-s is: 51.13 Mbs, the file-s for this book were downloaded 124 times, the file-s went public at Tue Sep 24 2013.
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2Group Theory And Quantum Mechanics
By Waerden, B. L. van der (Bartel Leendert), 1903-
This thesis is concerned with the representation theory of the Heisenberg group and its applications to both classical and quantum mechanics. We continue the development of $p$-mechanics which is a consistent physical theory capable of describing both classical and quantum mechanics simultaneously. $p$-Mechanics starts from the observation that the one dimensional representations of the Heisenberg group play the same role in classical mechanics which the infinite dimensional representations play in quantum mechanics. In this thesis we introduce the idea of states to $p$-mechanics. $p$-Mechanical states come in two forms: elements of a Hilbert space and integration kernels. In developing $p$-mechanical states we show that quantum probability amplitudes can be obtained using solely functions/distributions on the Heisenberg group. This theory is applied to the examples of the forced, harmonic and coupled oscillators. In doing so we show that both the quantum and classical dynamics of these systems can be derived from the same source. Also using $p$-mechanics we simplify some of the current quantum mechanical calculations. We also analyse the role of both linear and non-linear canonical transformations in $p$-mechanics. We enhance a method derived by Moshinsky for studying the passage of canonical transformations from classical to quantum mechanics. The Kepler/Coulomb problem is also examined in the $p$-mechanical context. In analysing this problem we show some limitations of the current $p$-mechanical approach. We then use Klauder's coherent states to generate a Hilbert space which is particularly useful for the Kepler/Coulomb problem.
“Group Theory And Quantum Mechanics” Metadata:
- Title: ➤ Group Theory And Quantum Mechanics
- Author: ➤ Waerden, B. L. van der (Bartel Leendert), 1903-
- Language: eng,ger
“Group Theory And Quantum Mechanics” Subjects and Themes:
- Subjects: Quantum theory - Group theory
Edition Identifiers:
- Internet Archive ID: grouptheoryquant0000waer
Downloads Information:
The book is available for download in "texts" format, the size of the file-s is: 367.60 Mbs, the file-s for this book were downloaded 212 times, the file-s went public at Tue Oct 27 2020.
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ACS Encrypted PDF - Cloth Cover Detection Log - DjVuTXT - Djvu XML - Dublin Core - EPUB - Item Tile - JPEG Thumb - JSON - LCP Encrypted EPUB - LCP Encrypted PDF - Log - MARC - MARC Binary - Metadata - OCR Page Index - OCR Search Text - PNG - Page Numbers JSON - Scandata - Single Page Original JP2 Tar - Single Page Processed JP2 ZIP - Text PDF - Title Page Detection Log - chOCR - hOCR -
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- Whefi.com: Download
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