A momentum representation treatment of the hydrogen atom problem with a generalized uncertainty relation,which leads to a minimal length (∆X i ) min = √ 3β + β ′ , is presented. We show that the distance squared operator can be factorized in the case β ′ = 2β. We analytically solve the s-wave bound-state equation. The leading correction to the energy spectrum caused by the minimal length depends on √ β. An upper bound for the minimal length is found to be about 10 −9fm. * Electronic address: djamilbouaziz@mail.univ-jijel.dz

We determine the energy spectrum and the corresponding eigenfunctions of a 2D Dirac oscillator in the presence of Aharonov-Bohm (AB) effect . It is shown that the energy spectrum depends on the spin of particle and the AB magnetic flux parameter. Finally, when the irregular solution occurs it is shown that the energy takes particular values. The nonrelativistic limit is also considered.

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Using the Lewis–Riesenfeld theory, we show that the time-dependent Schrödinger equation for non-central potentials with an arbitrary angular function U(θ) is analytically solvable. As a special case, we derive the exact solution for the double ring-shaped generalized non-central oscillator with time-dependent mass and frequency. The time-independent case, studied in the literature, is recovered.

We determine explicitly the exact transcendental bound states energies equation for a one-dimensional harmonic oscillator perturbed by a single and a double point interactions via Green’s function techniques using both momentum and position space representations. The even and odd solutions of the problem are discussed. The corresponding limiting cases are recovered. For the harmonic oscillator with a point interaction in more than one dimension, divergent series appear. We use to remove this divergence an exponential regulator and we obtain a transcendental equation for the energy bound states. The results obtained here are consistent with other investigations using different methods.