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A perturbative approach to Snyder space with applications

In this paper, we present a method for studying systems in the modified formulation of quantum mechanics known as Snyder space, proposed by Snyder (1947 Phys. Rev. 71 38–41). Snyder space predicts a modified commutation algebra for position and momentum operators. The method described in this paper introduces operators satisfying the canonical commutation relations and relates them to the position and momentum operators of Snyder space, effectively mapping a problem in Snyder space into a similar problem in standard quantum mechanics. The method is applied to the simple harmonic oscillator (SHO) in one and two dimensions as well as to the one-dimensional infinite square well. The energy spectra are calculated perturbatively for the SHO. We also find an exact spectrum for the one-dimensional infinite square well potential. These results are shown to agree with similar results found elsewhere in the literature.