An example of interplay between Physics and Mathematics: Exact resolution of a new class of Riccati Equations

摘要

AbstractA 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 time-dependent 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.Highlights?A resolutive strategy for Liouville SU(2) dynamical problems is used to solve DREs.?A new class of exactly solvable Riccati equations is reported.?Many examples illustrate our method and provide explicit solutions of selected DREs.]]>