Qualitative analysis of certain generalized classes of quadratic oscillator systems

Bagchi, B.; Ghosh, Samiran; Pal, Biswajit; Poria, Swarup

doi:10.1063/1.4939486

Cited by 6 publications

(1 citation statement)

References 27 publications

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“…The generalization of this system to n = 2 and n > 2 dimensions (and also for both λ > 0 and λ < 0) was studied in [46]. Since then it has been studied by different authors [47][48][49][50][51][52][53][54][55][56][57][58].…”

Section: Nonlinear Quasi-harmonic Oscillator With a Pdmmentioning

confidence: 99%

Quantization of Hamiltonian systems with a position dependent mass: Killing vector fields and Noether momenta approach

Cariñena¹,

Rañada²,

Santander³

2017

J. Phys. A: Math. Theor.

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The quantization of systems with a position dependent mass (PDM) is studied. We present a method that starts with the study of the existence of Killing vector fields for the PDM geodesic motion (Lagrangian with a PDM kinetic term but without any potential) and the construction of the associated Noether momenta. Then the method considers, as the appropriate Hilbert space, the space of functions that are square integrable with respect to a measure related with the PDM and, after that, it establishes the quantization, not of the canonical momenta p, but of the Noether momenta P instead. The quantum Hamiltonian, that depends on the Noether momenta, is obtained as an Hermitian operator defined on the PDM Hilbert space. In the second part several systems with position-dependent mass, most of them related with nonlinear oscillators, are quantized by making use of the method proposed in the first part.

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