The Power Quantum Calculus
In this chapter we introduce the power difference calculus based on the operator \(D_{n,q} [f](t) = \frac{f(qt^n)-f(t)}{qt^n -t}\) , where \(n\) is an odd positive integer and \(0
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Agnieszka B. Malinowska Delfim F. M. Torres
Quantum Variational Calculus
SpringerBriefs in Electrical and Computer Engineering Control, Automation and Robotics
Series editors Tamer Basar, Urbana, USA Antonio Bicchi, Pisa, Italy Miroslav Krstic, La Jolla, USA
For further volumes: http://www.springer.com/series/10198
Agnieszka B. Malinowska Delfim F. M. Torres
Quantum Variational Calculus
123
Agnieszka B. Malinowska Department of Mathematics Bialystok University of Technology, Faculty of Computer Science Bialystok Poland
ISSN 2191-8112 ISBN 978-3-319-02746-3 DOI 10.1007/978-3-319-02747-0
Delfim F. M. Torres Department of Mathematics University of Aveiro Aveiro Portugal
ISSN 2191-8120 (electronic) ISBN 978-3-319-02747-0 (eBook)
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Preface
Many physical phenomena are described by equations involving nondifferentiable functions, e.g., generic trajectories of quantum mechanics (Feynman and Hibbs 1965). Several different approaches to deal with nondifferentiable functions are proposed in the literature of variational calculus. W
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