A position-dependent mass model for the Thomas–Fermi potential: Exact solvability and relation to -doped semiconductors

2013 ◽  
Vol 333 ◽  
pp. 323-334 ◽  
Author(s):  
Axel Schulze-Halberg ◽  
Jesús García-Ravelo ◽  
Christian Pacheco-García ◽  
José Juan Peña Gil
Keyword(s):  
Mass Model ◽  
Doped Semiconductors ◽  
Exact Solvability ◽  
Thomas Fermi ◽  
Dependent Mass ◽  
Position Dependent Mass

scholarly journals PDM Damped-Driven Oscillators: Exact Solvability, Classical States Crossings, and Self-Crossings

2021 ◽  
Author(s):  
Omar Mustafa
Keyword(s):  
Harmonic Oscillator ◽  
Force Field ◽  
Dissipative Force ◽  
Classical Particle ◽  
Point Canonical Transformation ◽  
Exact Solvability ◽  
Classical State ◽  
Dependent Mass ◽  
Position Dependent Mass ◽  
Classical States

Abstract Within the standard Lagrangian and Hamiltonian setting, we consider a position-dependent mass (PDM) classical particle performing a damped driven oscillatory (DDO) motion under the influence of a conservative harmonic oscillator force field $V\left( x\right) =\frac{1}{2}\omega ^{2}Q\left( x\right) x^{2}$ and subjected to a Rayleigh dissipative force field $\mathcal{R}\left( x,\dot{x}\right) =\frac{1}{2}b\,m\left( x\right) \dot{x}^{2}$ in the presence of an external periodic (non-autonomous) force $F\left( t\right) =F_{\circ }\,\cos \left( \Omega t\right) $. Where, the correlation between the coordinate deformation $\sqrt{Q(x)}$ and the velocity deformation $\sqrt{m(x)}$ is governed by a point canonical transformation $q\left( x\right) =\int \sqrt{m\left( x\right) }dx=\sqrt{%Q\left( x\right) }x$. Two illustrative examples are used: a non-singular PDM-DDO, and a power-law PDM-DDO models. Classical-states $\{x(t),p(t)\}$ crossings are analysed and reported. Yet, we observed/reported that as a classical state $\{x_{i}(t),p_{i}(t)\}$ evolves in time it may cross itself at an earlier and/or a later time/s.

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