Publication Type : Journal Article
Publisher : Pramana
Source : Pramana, Volume 73, Number 6, p.969 (2009)
Url : http://dx.doi.org/10.1007/s12043-009-0173-x(link is external)
Keywords : quasi-bound states, Resonant tunnelling, Twin symmetric barrier
Campus : Coimbatore
School : School of Engineering
Department : Sciences
Year : 2009
Abstract : In analogy with the definition of resonant or quasi-bound states used in three-dimensional quantal scattering, we define the quasi-bound states that occur in one-dimensional transmission generated by twin symmetric potential barriers and evaluate their energies and widths using two typical examples: (i) twin rectangular barrier and (ii) twin Gaussian-type barrier. The energies at which reflectionless transmission occurs correspond to these states and the widths of the transmission peaks are also the same as those of quasi-bound states. We compare the behaviour of the magnitude of wave functions of quasi-bound states with those for bound states and with the above-barrier state wave function. We deduce a Breit-Wigner-type resonance formula which neatly describes the variation of transmission coefficient as a function of energy at below-barrier energies. Similar formula with additional empirical term explains approximately the peaks of transmission coefficients at above-barrier energies as well. Further, we study the variation of tunnelling time as a function of energy and compare the same with transmission, reflection time and Breit-Wigner delay time around a quasi-bound state energy. We also find that tunnelling time is of the same order of magnitude as lifetime of the quasi-bound state, but somewhat larger.
Cite this Research Publication : Dr. Umamaheswari A., Prema, P., Dr. Mahadevan S., and Shastry, C. S., “Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers”, Pramana, vol. 73, p. 969, 2009.