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Resonance

Resonant Transmission Through Rectangular Potential Well

S. Bose, J. Mitra, P. Mandal

Published Feb 25, 2026• 0 citations
Publisher
DOI
10.1007/s12045-026-1940-4

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We consider the bilayer heterostructure composed of the layer described by a rectangle-like potential and the background layer with an arbitrary potential profile given only by a transmission matrix. The conditions for the perfect (zero reflection) transmission of quantum particles across this structure is derived in the form of two basic equations on the rectangular layer parameters and the distance between the layers. The solution of these equations is analyzed in detail including some special cases and squeezing approximations. The effect of a rectangular well potential on the tunneling of particles with infinitesimally low energy through the background layer is investigated.
In this paper, we calculate the transmission and reflection amplitudes of wave functions for different potentials such as the delta function, the rectangular barrier, the Eckart potential, and the Hulthen potential. We describe the relationship between these amplitudes and compute the reflection resonances between each potential. We describe the transmission and reflection probabilities using the WKB formula and compare the results with ones obtained from matching the boundary conditions. Furthermore, we use a two by two transfer matrix to calculate a rigorous bound on the transmission and reflection probabilities.