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CQMechanics: A Unification of Quantum & Classical Mechanics: Quantum/Semi-Classical Entanglement, Quantum/Classical Path Integrals, by Stephen Blaha

CQMechanics: A Unification of Quantum & Classical Mechanics: Quantum/Semi-Classical Entanglement, Quantum/Classical Path Integrals,

by Stephen Blaha
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Book cover type: Hardcover
  • ISBN13: 9780997076189
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: Pingree-Hill Publishing
  • Publisher Imprint: Pingree-Hill Publishing
  • Publication Date:
  • Pages: 156
  • Original Price: GBP 24.0
  • Language: English
  • Edition: N/A
  • Item Weight: 490 grams
  • BISAC Subject(s): Physics / Mathematical & Computational

The relation of quantum and classical phenomena has been a subject of continuing interest. Most studies approximate the quantum description of a phenomenon to obtain a classical or semi-classical approximation. This book develops a new formalism that contains both fully quantum and classical sectors, and a continuous transformation between them that provides an intermediate partly quantum - partly classical sector. This intermediate sector can play the role of a bridge between the quantum and classical descriptions of a process. Using this new formalism we consider the case of the harmonic oscillator in detail relating the quantum oscillator through the bridge to the classical oscillator. We then develop a generalization of the Feynman path integral formalism that has both a normal quantum sector and also a 'new' classical path integral sector - again with a partly quantum-partly classical intermediate sector. Our path integral generalization yields a generalization of the Schroedinger equation with both quantum and classical 'wave function' solutions. We also apply this formalism to the Fokker-Planck equation, for which it is naturally adapted. Next we apply the new formalism to quantum field theories that are known to be chaotic, and then generate a classical sector - also with chaotic behavior. We also take the standard approach to quantum entanglement and show how to extract a semi-classical entanglement as well as a classical limit without entanglement. The Boltzmann equation is easily placed within the framework of our new formalism. We solve a special case of the Vlasov equation as an example. A special relativistic Boltzmann equation is also developed within the framework of our formalism. Lastly, we develop our formalism for boson and fermion quantum field theory. We give a sensible reason why Nature must be quantum.

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