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

机译:物理与数学之间相互作用的一个例子:精确   一类新的Riccati方程的解析

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摘要

A novel recipe for exactly solving in finite terms a class of specialdifferential Riccati equations is reported. Our procedure is entirely based ona successful resolution strategy quite recently applied to quantum dynamicaltime-dependent SU(2) problems. The general integral of exemplary differentialRiccati equations, not previously considered in the specialized literature, isexplicitly determined to illustrate both mathematical usefulness and easinessof applicability of our proposed treatment. The possibility of exploiting thegeneral integral of a given differential Riccati equation to solve an SU(2)quantum dynamical problem, is succinctly pointed out.
机译:报告了一种新颖的配方,用于精确地解决一类特殊的微分Riccati方程。我们的程序完全基于最近成功应用于量子动力学时间相关SU(2)问题的成功解决策略。明确确定示例性微分Riccati方程的一般积分,以前在专门文献中未曾考虑过,以说明我们提出的处理方法的数学实用性和适用性。简要指出了利用给定微分Riccati方程的一般积分解决SU(2)量子动力学问题的可能性。

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