@article{82ab29e1819047d3b3e8481eee8bd731,

title = "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 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.",

keywords = "Riccati equation, Solvable model, Time-dependent Hamiltonian, Unitary evolution",

author = "Markovich, {L. A.} and R. Grimaudo and A. Messina and H. Nakazato",

note = "Funding Information: A. Messina and R. Grimaudo warmly thank Prof. A. Klimov and Prof. M. Kus for interesting and stimulating discussions about the argument. H. N. was supported by the Waseda University Grant for Special Research Projects (No. 2016B-173 ). The study in Sections 2 and 3 by Markovich L.A. was supported by the Russian Science Foundation grant ( 14-50-00150 ). R. G. was partially supported by research funds in memory of Francesca Palumbo ( DiFC 3100050001D08+ ). Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

month = oct,

doi = "10.1016/j.aop.2017.07.008",

language = "English",

volume = "385",

pages = "522--531",

journal = "Annals of Physics",

issn = "0003-4916",

publisher = "Academic Press Inc.",

}