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

L. A. Markovich, R. Grimaudo, A. Messina, Hiromichi Nakazato

    Research output: Contribution to journalArticle

    10 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)522-531
    Number of pages10
    JournalAnnals of Physics
    Volume385
    DOIs
    Publication statusPublished - 2017 Oct 1

    Keywords

    • Riccati equation
    • Solvable model
    • Time-dependent Hamiltonian
    • Unitary evolution

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

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