Impact of the non-canonical approach to the exact solution of the ideal one-dimensional electron gas confined with an anisotropic quantum wire of oscillator-shaped profile

Abstract

We study an exactly solvable model that can be interpreted as an ideal one-dimensional electron gas confined with an anisotropic quantum wire potential of oscillator-shaped profile. The homogeneous nature of the quantum wire is broken by the introduction of the effective electron mass, which changes with radial distance. We solve the problem described both within the canonical and the non-canonical approach. Analytical expressions of the wavefunctions of the stationary states for both cases in terms of the Laguerre polynomials are obtained, as well as the discrete energy spectrum related to these wavefunctions. Additionally, an exact solution to the angular position part of the position-dependent mass Schrödinger equation within the non-canonical approach leads to the angular-part wavefunctions of the even and odd states expressed through the Gegenbauer polynomials. Possible limit relations and special cases are studied too.

21 pages, 4 figures

References in corpus (12)

• Full configuration interaction approach to the few-electron problem in artificial atoms
• Ordering ambiguity revisited via position dependent mass pseudo-momentum operators
• Localization Transition in a Ballistic Quantum Wire
• Dunkl-Graphene in constant magnetic field
• Ideal Bose Gas and Blackbody Radiation in the Dunkl Formalism
• Exact solution of the position-dependent effective mass and angular frequency Schrödinger equation: harmonic oscillator model with quantized confinement parameter
• The Wigner distribution function for the one-dimensional parabose oscillator
• Experimental realization of para-particle oscillators
• The Wigner function of a semiconfined harmonic oscillator model with a position-dependent effective mass
• Energy eigenstates of position-dependent mass particles in a spherical quantum dot
• Deformation of the Heisenberg-Weyl algebra and the Lie superalgebra $\mathfrak{osp}\left(1|2\right)$: exact solution for the quantum harmonic oscillator with a position-dependent mass
• Bounding the Wigner Deformation Parameter in Harmonically Trapped Bose Gases