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

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

Research output: Contribution to journalArticlepeer-review

13 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

Keywords

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

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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