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

TL;DR

This paper introduces a new exact solution method for a class of Riccati differential equations, demonstrating its mathematical utility and potential applications in quantum physics.

Contribution

It presents a novel, finite-term solution strategy for Riccati equations inspired by quantum dynamical problem-solving techniques.

Findings

Explicit general integrals for new Riccati equations

Application to quantum SU(2) problems

Demonstrates ease and usefulness of the method

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 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.