# References to Mechanics (Classical, Quantum, Statistical) using Time-Scale calculus?

Time-Scale Calculus, is a theory which unifies ordinary (plus fractional and q-) calculus with discrete (and finite differences) calculus.

In a sense, in a similar way the Lebesgue integral (or Riemann–Stieltjes integral) unifies both continous integration and discrete summation.

The rationale is to use time-scales (or measure chains) which include continous (dense) points and discrete or semi-discrete (scattered, isolated) points.

Even Variational Calculus (and Euler-Lagrange equations) and Noether's Theorem have been (recently) generalised (more or less) to time-scale calculus.

Any references to (unified) formulation of Mechanics (Classical, Quantum, Statistical) in time-scale calculus (and their relevance)?

UPDATE:

• Premise: I don't know this calculus very well. However I don't see how it may unify the formulation of e.g. classical and quantum mechanics. The dynamics is in both cases a differential equation (not a difference one). There are other mathematical aspects, in my opinion, that emphasize the relevant differences between the two theories (e.g. commutativity vs non-commutativity, non-linear vs linear dynamics). – yuggib Nov 7 '14 at 9:23
• @yuggib, one can say the main difference between clasical/quantum is the finite value of the planck constant $h$ (e.g Ehrenfest theorem). Furthermore there are indeed formal mechanics which are the same for both Classical/Quantum (and Statistical) (this is another question). In any case, "unified" is added extra, even mechanics (classical) references and their relevance is good – Nikos M. Nov 7 '14 at 9:39