Non-differentiable variational principles

Mathematics – General Mathematics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

20 pages

Scientific paper

We develop a calculus of variations for functionals which are defined on a set of non differentiable curves. We first extend the classical differential calculus in a quantum calculus, which allows us to define a complex operator, called the scale derivative, which is the non differentiable analogue of the classical derivative. We then define the notion of extremals for our functionals and obtain a characterization in term of a generalized Euler-Lagrange equation. We finally prove that solutions of the Schr\"odinger equation can be obtained as extremals of a non differentiable variational principle, leading to an extended Hamilton's principle of least action for quantum mechanics. We compare this approach with the scale relativity theory of Nottale, which assumes a fractal structure of space-time.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Non-differentiable variational principles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Non-differentiable variational principles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-differentiable variational principles will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-399407

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.