Abstract
Abstract 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 m = 1.
Highlights
We formulated the oscillators with positiondependent finite symmetric decreasing and increasing mass
In view of the importance of vibration and position-dependent mass (PDM), we focused our attention to study the vibration of a newly designed finite symmetric increasing and decreasing mass harmonic like oscillators using classical and quantum mechanical approaches
The existence of closed curve in classical phase portrait signifies that the system will admit discrete eigenvalues microscopically
Summary
Abstract: We formulated the oscillators with positiondependent finite symmetric decreasing and increasing mass. In semiconductors and other problems related to solid state physics, we mainly deal with atoms whose masses cannot be infinite or zero If it varies with distance, it must be within the finite values. Considering the above literature, we propose a new model position-dependent finite mass variation, i.e. for symmetric cases comprising of both increasing and decreasing PDM. In view of the importance of vibration and PDM, we focused our attention to study the vibration of a newly designed finite symmetric increasing and decreasing mass harmonic like oscillators using classical and quantum mechanical approaches. The rest of the present work is organized as follows: In Section 2, a classical description of the harmonic like oscillator comprising of both symmetric decreasing and increasing mass is discussed by performing analytical calculations.
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