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

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 $(\Delta X{)}_0=\hslash \sqrt{\beta }$, where $\beta$ 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.

References in corpus (4)

• Running Coupling with Minimal Length
• Casimir Effect in the Presence of Minimal Lengths
• One dimensional Coulomb-like problem in deformed space with minimal length
• Effect of Minimal lengths on Electron Magnetism

Cited by in corpus (5)

• Ground State of the Hydrogen Atom via Dirac Equation in a Minimal Length Scenario
• Exactly solvable problems in the momentum space with a minimum uncertainty in position
• Dirac $\delta$-function potential in quasiposition representation of a minimal-length scenario
• Exact Solution of Schrödinger Equation in (Anti-)de Sitter Spaces for Hydrogen Atom
• Relativistic Approach to the Hydrogen Atom in a Minimal Length Scenario