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

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

2007-07-13

arxiv.org/abs/0707.2043v2

J. Math. Phys 48, 112104 (2007)

Physics

Quantum Physics

Scientific paper

10.1063/1.2809267

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 $(\Delta X)_{0}=\hbar \sqrt{\beta}$, 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.

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