An example of interplay between Physics and Mathematics: Exact resolution of a new class of Riccati Equations
Abstract
A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical timedependent SU(2) problems. The general integral of exemplary differential Riccati equations, not previously considered in the specialized literature, is explicitly determined to illustrate both mathematical usefulness and easiness of applicability of our proposed treatment. The possibility of exploiting the general integral of a given differential Riccati equation to solve an SU(2) quantum dynamical problem, is succinctly pointed out.
 Publication:

Annals of Physics
 Pub Date:
 October 2017
 DOI:
 10.1016/j.aop.2017.07.008
 arXiv:
 arXiv:1710.09122
 Bibcode:
 2017AnPhy.385..522M
 Keywords:

 Riccati equation;
 Solvable model;
 Timedependent Hamiltonian;
 Unitary evolution;
 Mathematical Physics
 EPrint:
 10 pages