English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this paper, we investigate the quantum dynamics of underlying twoone-dimensional quadratic Li'enard type nonlinear oscillators which areclassified under the category of maximal (eight parameter) Lie point symmetrygroup (J. Math. Phys.54 , 053506 (2013)). Classically, both the systems werealso shown to be linearizable as well as isochronic. In this work, we study thequantum dynamics of the nonlinear oscillators by considering a general orderedposition dependent mass Hamiltonian. The ordering parameters of the mass termare treated to be arbitrary to start with. We observe that the quantum versionof these nonlinear oscillators are exactly solvable provided that the orderingparameters of the mass term are subjected to certain constraints imposed on thearbitrariness of the ordering parameters. We obtain the eigenvalues andeigenfunctions associated with both the systems. We also consider briefly thequantum versions of other examples of quadratic Li'enard oscillators which areclassically linearizable.

Quantum solvability of quadratic Li'enard type nonlinear oscillators  possessing maximal Lie point symmetries: An implication of arbitrariness of  ordering parameters