Nondifferentiable variational principles in terms of a quantum operator

Abstract

We develop Cresson's nondifferentiable calculus of variations on the space of Hölder functions. Several quantum variational problems are considered: with and without constraints, with one and more than one independent variable, of first and higher-order type.

Submitted 24-Apr-2011; revised 18-Jun-2011; accepted 20-Jun-2011; for publication in Mathematical Methods in the Applied Sciences

References in corpus (15)

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Cited by in corpus (1)

• Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus