A simple method for constructing non-liouvillian first integrals of autonomous planar systems

Schulze-Halberg, Axel

doi:10.1007/s10587-006-0074-9

Cited by 1 publication

(2 citation statements)

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“…The above Mathews-Lakshmanan oscillator may be considered as the zero-dimensional version of a scalar nonpolynomial field equation 1,23 . The literature shows evidence for a large interest over the system both from classical and quantum points of views [23][24][25][26][27][28][29][30][31][32] . The above oscillator is often considered as a nonlinear extension of the harmonic oscillator as the Hamiltonian in (8) tends to the harmonic oscillator Hamiltonian in the limit λ → 0.…”

Section: Mathews-lakshmanan Oscillatormentioning

confidence: 99%

“…In this article, we consider an interesting PDM system, namely the Mathews-Lakshmanan oscillator, and try to solve it for all possible orderings. The Mathews-Lakshmanan (ML) oscillator is a non-polynomial oscillator and has attracted considerable attention over the years [23][24][25][26][27][28][29][30][31][32][33] from different perspectives. The quantum solvability of this model has also been studied for particular orderings 1,34 .…”

Section: Introductionmentioning

confidence: 99%

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Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator

Karthiga

Ruby²,

Senthilvelan

et al. 2017

Journal of Mathematical Physics

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In position dependent mass (PDM) problems, the quantum dynamics of the associated systems have been understood well in the literature for particular orderings. However, no efforts seem to have been made to solve such PDM problems for general orderings to obtain a global picture.In this connection, we here consider the general ordered quantum Hamiltonian of an interesting position dependent mass problem, namely the Mathews-Lakshmanan oscillator, and try to solve the quantum problem for all possible orderings including Hermitian and non-Hermitian ones. The other interesting point in our study is that for all possible orderings, although the Schrödinger equation of this Mathews-Lakshmanan oscillator is uniquely reduced to the associated Legendre differential equation, their eigenfunctions cannot be represented in terms of the associated Legendre polynomials with integral degree and order. Rather the eigenfunctions are represented in terms of associated Legendre polynomials with non-integral degree and order. We here explore such polynomials and represent the discrete and continuum states of the system. We also exploit the connection between associated Legendre polynomials with non-integral degree with other orthogonal polynomials such as Jacobi and Gegenbauer polynomials.

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