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ERIC Number: EJ931296
Record Type: Journal
Publication Date: 2011-Mar
Pages: 19
Abstractor: As Provided
Reference Count: 28
ISSN: ISSN-0143-0807
Low-Dimensional Nanostructures and a Semiclassical Approach for Teaching Feynman's Sum-over-Paths Quantum Theory
Onorato, P.
European Journal of Physics, v32 n2 p259-277 Mar 2011
An introduction to quantum mechanics based on the sum-over-paths (SOP) method originated by Richard P. Feynman and developed by E. F. Taylor and coworkers is presented. The Einstein-Brillouin-Keller (EBK) semiclassical quantization rules are obtained following the SOP approach for bounded systems, and a general approach to the calculation of propagation amplitude is discussed for unbounded systems. These semiclassical results are obtained when the SOP is limited to the trajectories classically allowed. EBK semiclassical quantization and the topological Maslov index are used to deduce the correct quantum mechanical results for systems which live in a two-dimensional world as quantum dots and quantum rings. In the latter systems, the semiclassical propagation amplitude is used to discuss the Aharonov-Bohm effect. The development involves only elementary calculus and also provides a theoretical introduction to the quantum nature of low-dimensional nanostructures. (Contains 2 footnotes and 3 figures.)
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Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A