One-dimensional Coulomb-like problem in deformed space with minimal length. (English) Zbl 1084.81044

Fityo, T. V.; Vakarchuk, I. O.; Tkachuk, V. M.

J. Phys. A, Math. Gen. 39, No. 9, 2143-2149 (2006).

Summary: The spectrum and eigenfunctions in the momentum representation for a 1D Coulomb-like potential with deformed Heisenberg algebra leading to minimal length are found exactly. It is shown that the correction due to the deformation is proportional to the square root of the deformation parameter. We obtain the same spectrum using the Bohr–Sommerfeld quantization condition.

MSC:

81S10	Geometry and quantization, symplectic methods
53D55	Deformation quantization, star products
81Q10	Selfadjoint operator theory in quantum theory, including spectral analysis
81R15	Operator algebra methods applied to problems in quantum theory