Год выпуска: 2014 Автор: Sengul Nalc? and Oktay K. Pashaev Издательство: LAP Lambert Academic Publishing Страниц: 272 ISBN: 9783659619694
Описание
The quantum or q-calculus is based on finite difference re-scaling and first results in it belong to Euler and Gauss. Developed by Fermat, Jackson, Heine, Jacobi, Ramanujan etc, in XX century it was rediscovered as symmetry of quantum models related to quantum algebras and quantum groups. Noncommutative geometry, fractals, hydrodynamics and quantum theory are fields of its applications.The book is devoted to basic principles of q-caluculs and applications to classical and quantum linear and nonlinear problems. Starting from notion of q-number and q-derivative we study classical and quantum oscillators, heat and Burgers equations. We introduce the concepts of q-analogs of shock solitons, traveling waves and analytic functions, and develop multiple q-calculus to study multi-dimensional problems. By recognizing Fibonacci numbers as q-calculus with golden ratio bases, we construct nonlinear quantum oscillator with Fibonacci spectrum. The book is self contained and pedagogically written as...
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