Investigation of the Infinite Discrete Levels from Finite discrete Levels in Position Dependent Mass Quantum Systems

We find quantum systems having finite distinct discrete energy levels can reflect infinite distinct energy levels under suitable form of position dependent mass systems. A model example has been investigated considering the fractional Harmonic Oscillator [6]. In addition to this,we also notice the same behaviour in other quantum models. In all the cases, we find finite distinct discrete levels becoming infinite distinct discrete levels under position dependent mass quantum systems without the change in the potential energy.