Spectrum of the three dimensional fuzzy well
High Energy Physics - Theory
2015-06-22 v1 Mathematical Physics
math.MP
Quantum Physics
Abstract
We develop the formalism of quantum mechanics on three dimensional fuzzy space and solve the Schr\"odinger equation for a free particle, finite and infinite fuzzy wells. We show that all results reduce to the appropriate commutative limits. A high energy cut-off is found for the free particle spectrum, which also results in the modification of the high energy dispersion relation. An ultra-violet/infra-red duality is manifest in the free particle spectrum. The finite well also has an upper bound on the possible energy eigenvalues. The phase shifts due to scattering around the finite fuzzy potential well have been calculated.
Keywords
Cite
@article{arxiv.1407.5857,
title = {Spectrum of the three dimensional fuzzy well},
author = {N Chandra and H W Groenewald and J N Kriel and F G Scholtz and S Vaidya},
journal= {arXiv preprint arXiv:1407.5857},
year = {2015}
}