Asymmetric quantum wells and the solotone effect: towards an inverse method
- 11 October 2021
- journal article
- research article
- Published by IOP Publishing in European Journal of Physics
- Vol. 42 (6), 065407
- https://doi.org/10.1088/1361-6404/ac247d
Abstract
In previous work the author considered heat conduction in a one-dimensional composite rod. The rod consisted of three parts and two different materials. Boundary and interface conditions were imposed and the eigenvalues computed numerically. This undertaking resulted in the first demonstration, within a heat conduction context, of the presence of oscillations within the eigenvalue distribution. This so-called solotone effect arises when the underlying differential equations contain discontinuities within their coefficients. Furthermore, a novel inverse method was presented and used to accurately estimate the relative thermophysical properties of a composite rod. This was achieved by examining the periodicity of the solotone effect. In this paper we demonstrate, for the first time, the existence of a solotone effect within the energy eigenvalues of a quantum well. At first sight there appears to be little connection between classical heat conduction and quantum mechanics. Nevertheless, these phenomena are related since in both situations the underlying equations may be expressed in Sturm-Liouville form. Our analysis will focus on an asymmetric infinite square well containing a particle with position dependent mass. This arrangement is sufficiently discontinuous to give rise to a solotone effect, and we believe this effect could be used to infer information about the properties of a potential well. However, we stop short of developing a complete inverse method since we believe an investigation of this nature would make for an interesting undergraduate project.Keywords
This publication has 13 references indexed in Scilit:
- Inverse method identification of thermophysical properties based on solotone effect analysis for discontinuous Sturm–Liouville systemsInverse Problems in Science and Engineering, 2018
- The infinite well and Dirac delta function potentials as pedagogical, mathematical and physical models in quantum mechanicsPhysics Reports, 2014
- “Smart Design” of Quantum Wells and Double-Quantum Wells StructuresWorld Journal of Condensed Matter Physics, 2014
- More on the asymmetric infinite square well: energy eigenstates with zero curvatureEuropean Journal of Physics, 2005
- Comparing classical and quantum probability distributions for an asymmetric infinite wellEuropean Journal of Physics, 2000
- Femtosecond Infrared Emission Resulting from Coherent Charge Oscillations in Quantum WellsPhysical Review Letters, 1996
- Deviations from the normal mode spectrum of asymptotic theoryAstrophysics and Space Science, 1986
- Asymptotic behavior of the eigenvalues of a Sturm-Liouville system with discontinuous coefficientsJournal of Mathematical Analysis and Applications, 1976
- The Effect of Discontinuities in Density and Rigidity on Torsional Eigenfrequencies of the EarthGeophysical Journal International, 1975
- Asymptotic Structure in Torsional Free Oscillations of the Earth-I. Overtone StructureGeophysical Journal International, 1974