Journal
AMERICAN JOURNAL OF PHYSICS
Volume 81, Issue 2, Pages 104-111Publisher
AMER ASSOC PHYSICS TEACHERS AMER INST PHYSICS
DOI: 10.1119/1.4765628
Keywords
band structure; physics education; probability; quantum theory; teaching
Funding
- CONACYT [S-4130, S-3158]
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The quantum mechanical transmission probability is calculated for one-dimensional finite lattices with three types of potentials: periodic, quasiperiodic, and random. When the number of lattice sites included in the computation is systematically increased, distinct features in the transmission probability vs. energy diagrams are observed for each case. The periodic lattice gives rise to allowed and forbidden transmission regions that correspond to the energy band structure of the infinitely periodic potential. In contrast, the transmission probability diagrams for both quasiperiodic and random lattices show the absence of well-defined band structures and the appearance of wave localization effects. Using the average transmissivity concept, we show the emergence of exponential (Anderson) and power-law bounded localization for the random and quasiperiodic lattices, respectively. (C) 2013 American Association of Physics Teachers. [http://dx.doi.org/10.1119/1.4765628]
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