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arXiv · 0707.2043

Coulomb potential in one dimension with minimal length: A path integral approach

Khireddine Nouicer
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Abstract

We solve the path integral in momentum space for a particle in the field of the Coulomb potential in one dimension in the framework of quantum mechanics with the minimal length given by $(ΔX)_{0}=\hbar \sqrtβ$, where $β$ is a small positive parameter. From the spectral decomposition of the fixed energy transition amplitude we obtain the exact energy eigenvalues and momentum space eigenfunctions.

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Khireddine Nouicer. 2007-11-23. Coulomb potential in one dimension with minimal length: A path integral approach. https://doi.org/10.1063/1.2809267

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