6533b86dfe1ef96bd12ca065

RESEARCH PRODUCT

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

Roberto GrimaudoL. A. MarkovichHiromichi NakazatoAntonino Messina

subject

Time-dependent HamiltonianClass (set theory)Solvable modelUnitary evolution.010102 general mathematicsGeneral Physics and AstronomyFOS: Physical sciencesMathematical Physics (math-ph)01 natural sciencesSettore FIS/03 - Fisica Della MateriaRiccati equation0103 physical sciencesComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONRiccati equationApplied mathematicsDifferential riccati equations0101 mathematics010306 general physicsQuantumDifferential (mathematics)Mathematical PhysicsMathematicsResolution (algebra)

description

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.

yearjournalcountryeditionlanguage
2017-10-25
10.1016/j.aop.2017.07.008http://hdl.handle.net/10447/314397