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Semi-infinite Quantum Wells In a Position-Dependent Mass Background

C. Quesne

arXiv:2210.15502Quantum Studies Mathematics and FoundationsJan 11, 20238 citations

Information-theoretic spreading measures of a particle confined in a 3D infinite spherical well

Debraj Nath, Ramon Carbó‐Dorca

Journal of Mathematical ChemistryMar 5, 20235 citations

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

Biswanath Rath, Jihad Asad, Hussein Shanak +2 more

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.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.

European Journal of Pure and Applied MathematicsJan 31, 20220 citations

Investigation of the non-relativistic fermi-gas model by considering the position-dependent mass

Soroush Zare, M. de Montigny, HASSAN HASSANABADI

We investigate the Schrödinger equation in the position-dependent mass framework with an infinite square well potential. We apply this approach to a Fermi gas, calculate the density of states of the gas, examine the information entropy, some expectation values and the uncertainty principle.

Journal of the Korean Physical SocietyJan 1, 20172 citations

Quantum information entropies for position-dependent mass Schrödinger problem

G. Yáñez-Navarro, Guo-Hua Sun, T. Dytrych +3 more

Annals of PhysicsJun 3, 2014109 citations

Displacement operator for quantum systems with position-dependent mass

R. N. Costa Filho, Murilo Pereira de Almeida, G. A. Farias +1 more

A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique commutation relation for $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{x}$ and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{p}}_{\ensuremath{\gamma}}$. Such a formalism naturally leads to a Schr\"odinger-like equation that is reminiscent of wave equations typically used to model electrons with position-dependent (effective) masses propagating through abrupt interfaces in semiconductor heterostructures. The distinctive features of our approach are demonstrated through analytical solutions calculated for particles under null and constant potentials like infinite wells in one and two dimensions and potential barriers.A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique commutation relation for $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{x}$ and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{p}}_{\ensuremath{\gamma}}$. Such a formalism naturally leads to a Schr\"odinger-like equation that is reminiscent of wave equations typically used to model electrons with position-dependent (effective) masses propagating through abrupt interfaces in semiconductor heterostructures. The distinctive features of our approach are demonstrated through analytical solutions calculated for particles under null and constant potentials like infinite wells in one and two dimensions and potential barriers.

arXiv:1110.1582Physical Review ANov 22, 2011127 citations

Information-theoretic measures for a position-dependent mass system in an infinite potential well

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