Path Integration in Conical Space

Details Path Integration in Conical Space Path Integration in Conical Space

2011-10-11

arxiv.org/abs/1110.2279v2

Physics

Mathematical Physics

Scientific paper

10.1016/j.physleta.2011.11.019

Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical space can be reduced to a form identical with that in flat space when the discrete angular momentum of each partial wave is replaced by a specific non-integral angular momentum. The effective potential is found proportional to the squared mean curvature of the conical surface embedded in Euclidean space. The path integral calculation is compatible with the Schr\"odinger equation modified with the Gaussian and the mean curvature.

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