Position-dependent finite symmetric mass harmonic like oscillator: Classical and quantum mechanical study

We formulated the oscillators with position-dependent finite symmetric decreasing and increasing mass. The classical phase portraits of the systems were studied by analytical approach (He’s frequency formalism). We also study the quantum mechanical behaviour of the system and plot the quantum mechan...

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Bibliographic Details
Published in:Open Physics 2021-05, Vol.19 (1), p.266-276
Main Authors: Rath, Biswanath, Mallick, Pravanjan, Mohapatra, Prachiprava, Asad, Jihad, Shanak, Hussein, Jarrar, Rabab
Format: Article
Language:English
Subjects:
classical mechanics
harmonic oscillator
position-dependent mass
quantum mechanics
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Summary:We formulated the oscillators with position-dependent finite symmetric decreasing and increasing mass. The classical phase portraits of the systems were studied by analytical approach (He’s frequency formalism). We also study the quantum mechanical behaviour of the system and plot the quantum mechanical phase space for necessary comparison with the same obtained classically. The phase portrait in all the cases exhibited closed loop reflecting the stable system but the quantum phase portrait exhibited the inherent signature (cusp or kink) near origin associated with the mass. Although the systems possess periodic motion, the discrete eigenvalues do not possess any similarity with that of the simple harmonic oscillator having = 1.
ISSN:2391-5471
2391-5471
DOI:10.1515/phys-2021-0024