Quantization Methods in the Theory of Differential Equations

Quantization Methods in the Theory of Differential Equations

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This volume presents a systematic and mathematically rigorous exposition of methods for studying linear partial differential equations. It focuses on quantization of the corresponding objects (states, observables and canonical transformations) in the phase space. The quantization of all three types of classical objects is carried out in a unified way with the use of a special integral transform. This book covers recent as well as established results, treated within the framework of a universal approach. It also includes applications and provides a useful reference text for graduate and research-level readers.Accordingly, the asymptotic solution cannot be obtained in the form of a (regular) series in powers of the parameter (which would be the case for regular perturbations). ... The aquot;quantum-mechanicalaquot; nature of these problems however need not be apparent, and in the main text we shall ... It applies to simplest classical systems with phase space R2n and the standard Poisson bracket for the observables.4anbsp;...

Title:Quantization Methods in the Theory of Differential Equations
Author:Vladimir E. Nazaikinskii, B.-W. Schulze, Boris Yu. Sternin
Publisher:CRC Press - 2002-05-16


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