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International Journal of Modern Physics A

Path integral approach to theD-dimensional quantum mechanics of the nonrelativistic Snyder–de Sitter model

H. Benzair, Tahar Boudjedaa, M. Merad

Published Oct 9, 2020• 7 citations
Publisher

Abstract

In the context of Snyder–de Sitter (SdS) algebra, we formulate the D-dimensional momentum space path integral transition amplitude for harmonic oscillator and free particle. The exact energy spectrum and the corresponding normalized radial momentum space eigenfunctions are obtained through the different quantum corrections rule.
DOI
10.1142/s0217751x20501808

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As an alternative formulation of quantum mechanics, path integral is based on the notion of transition amplitude which gives the wave function of a quantum system at a time t f by acting on the wave function at an earlier time ti.We show that for a general quadratic form for the Lagrangian of the system, transition amplitude has the form f (t f -ti)e i h S class., where S class. is the classical action.We then present an algebraic method to evaluate the function f (t f -ti) without refereing to the path integral calculations.We examine the presented method to the cases of free particle and harmonic oscillator and obtain their propagators.