Spectrum of the three dimensional fuzzy well

Abstract

We develop the formalism of quantum mechanics on three dimensional fuzzy space and solve the Schrödinger 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.

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• Equilibrium properties of blackbody radiation with an ultraviolet energy cut-off
• Pinhole interference in three-dimensional fuzzy space
• Super-Chandrasekhar limiting mass white dwarfs as emergent phenomena of noncommutative squashed fuzzy spheres
• Noncommutativity in Configuration Space Induced by A Conjugate Magnetic Field in Phase Space
• Massive Neutron Stars and White Dwarfs as Noncommutative Fuzzy Spheres