A note on the one-dimensional hydrogen atom with minimal length uncertainty

Understand

We present exact energy spectrum and eigenfunctions of the one-dimensional hydrogen atom in the presence of the minimal length uncertainty.

• By requiring the self-adjointness property of the Hamiltonian, we completely determine the quantization condition.
• We indicate that the single-valuedness criteria of the eigenfunctions in non-deformed case is an emergent condition and the semiclassical solutions exactly coincide with the quantum mechanical results.
• The behavior of the wave functions at the origin in coordinate space and in quasiposition space is discussed finally.