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- Title
Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers.
- Authors
Maheswari, A. Uma; Prema, P.; Mahadevan, S.; Shastry, C. S.
- 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.
- Subjects
QUASIANALYTIC functions; WAVE functions; RESONANCE; QUANTUM theory; GAUSSIAN basis sets (Quantum mechanics)
- Publication
Pramana: Journal of Physics, 2009, Vol 73, Issue 6, p969
- ISSN
0304-4289
- Publication type
Article
- DOI
10.1007/s12043-009-0173-x