Tailor-made Quantum Well-in-a-Well Systems: Their Bound States and Scattering Properties

TL;DR

This study investigates the bound states and scattering properties of custom-designed quantum well-in-a-well systems, revealing how modifications in well size affect energy levels and transmission probabilities using numerical methods.

Contribution

It introduces a method to construct and analyze tailored quantum well-in-a-well systems with detailed insights into their spectral and scattering characteristics.

Findings

Decreasing the middle well size lowers the ground state energy.

More bound states appear and become more evenly spaced with smaller embedded wells.

Transmission probability is lowest for systems with larger embedded wells.

Abstract

The resulting stationary states and scattering properties of an effective potential brought about by embedding a quantum well in another well are investigated in this work. The composite well system is constructed via a superposition of modified Poeschl - Teller potential wells. The energy spectrum in each composite well is obtained using the shooting method and the transport of a particle above this system is analyzed using the transfer matrix method. It is shown that decreasing the size of the embedded middle well lowers the ground state energy of the well-in-a-well system. Moreover, the bound states increase in number and become more evenly spaced. In addition, the transmission probability of a free particle incident above a composite well is lowest for the system with a large embedded well as compared to well-in-a-well systems of the same depth. Small variations in designed potential wells yield different quantum mechanical features.