One-dimensional Coulomb-like problem in general case of deformed space with minimal length

Abstract

We present a definition of the two-sided inverse of position operator in general case of deformed Heisenberg algebra leading to minimal length. Energy spectrum and eigenfunctions in momentum space for 1D Coulomb-like potential in deformed space are found exactly. We analyse the energy spectrum for different partial cases of deformation function and find that correction due to the deformation highly depends on type of the deformation function.

12 pages

References in corpus (3)

• One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum
• A note on the one-dimensional hydrogen atom with minimal length uncertainty
• Exactly solvable problems in the momentum space with a minimum uncertainty in position

Cited by in corpus (4)

• Exact solutions for two-body problems in 1D deformed space with minimal length
• Integral Transforms and $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians
• Regularization of ${\delta }^{\prime }$ potential in general case of deformed space with minimal length
• Exact continuity equation in a space with minimal length