Quantum Mechanics on Curved Hypersurfaces

Details Quantum Mechanics on Curved Hypersurfaces Quantum Mechanics on Curved Hypersurfaces

2010-10-11

arxiv.org/abs/1010.2079v1

Physics

High Energy Physics

High Energy Physics - Theory

39 pages, M. Sc. Thesis, incorporates minor corrections in the text

Scientific paper

In this work, Schr\"odinger and Dirac equations will be examined in geometries that confine the particles to hypersurfaces. For this purpose, two methods will be considered. The first method is the thin layer method which relies on explicit use of geometrical relations and the squeezing of a certain coordinate of space (or spacetime). The second is Dirac's quantization procedure involving the modification of canonical quantization making use of the geometrical constraints. For the Dirac equation, only the first method will be considered. Lastly, the results of the two methods will be compared and some notes on the differences between the results will be included.

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