### 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 language | English |
---|---|

Pages (from-to) | 522-531 |

Number of pages | 10 |

Journal | Annals of Physics |

Volume | 385 |

DOIs | |

Publication status | Published - 2017 Oct 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*385*, 522-531. https://doi.org/10.1016/j.aop.2017.07.008

**An example of interplay between Physics and Mathematics : Exact resolution of a new class of Riccati Equations.** / Markovich, L. A.; Grimaudo, R.; Messina, A.; Nakazato, Hiromichi.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 385, pp. 522-531. https://doi.org/10.1016/j.aop.2017.07.008

}

TY - JOUR

T1 - An example of interplay between Physics and Mathematics

T2 - Exact resolution of a new class of Riccati Equations

AU - Markovich, L. A.

AU - Grimaudo, R.

AU - Messina, A.

AU - Nakazato, Hiromichi

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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.

AB - 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.

KW - Riccati equation

KW - Solvable model

KW - Time-dependent Hamiltonian

KW - Unitary evolution

UR - http://www.scopus.com/inward/record.url?scp=85033369508&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85033369508&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2017.07.008

DO - 10.1016/j.aop.2017.07.008

M3 - Article

AN - SCOPUS:85033369508

VL - 385

SP - 522

EP - 531

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

ER -