Triangular Quantum Profiles: transmission probability and energy spectrum
Altug Arda
TL;DR
This paper derives analytical formulas for transmission probabilities and energy spectra in 1D quantum systems with position-dependent mass, focusing on triangular barriers and wells, validated through numerical examples for GaAs heterostructures.
Contribution
It provides new analytical solutions for quantum transmission and energy spectra in systems with position-dependent mass, using Airy and Kummer functions.
Findings
Analytical expressions for transmission probability and energy spectrum are obtained.
The formulas are validated with numerical examples for GaAs heterostructures.
The approach extends understanding of quantum transport in heterostructures.
Abstract
Analytical expressions for the transition probability and the energy spectrum of the 1D Schr\"odinger equation with position dependent mass are presented for the triangular quantum barrier and quantum well. The transmission coefficient is obtained by using the wave functions written in terms of the Airy's functions and of the solutions of the Kummer's differential equation. In order to show the validity of our analyze, an example by taking some numerical values for GaAs heterostructure is presented.
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