Parametric oscillators from factorizations employing a constant-shifted Riccati solution of the harmonic oscillator

Details Parametric oscillators from factorizations employing a constant-shifted Riccati solution of the harmonic oscillator Parametric oscillators from factorizations employing a constant-shifted Riccati solution of the harmonic oscillator

2010-08-09

arxiv.org/abs/1008.1441v3

Phys. Lett. A375: 3491-3495,2011

Physics

Mathematical Physics

11 pages, 4 figures, published version

Scientific paper

10.1016/physleta.2011.08.024

We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic oscillator. The mathematical results show that some of these oscillators could be of physical nature. We give the solutions of the obtained second-order differential equations and the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry. Possible applications are mentioned

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