Search results for "Momentum space"

On the discreet spectrum of fractional quantum hydrogen atom in two dimensions

2019

We consider a fractional generalization of two-dimensional (2D) quantum-mechanical Kepler problem corresponding to 2D hydrogen atom. Our main finding is that the solution for discreet spectrum exists only for $\mu>1$ (more specifically $1 < \mu \leq 2$, where $\mu=2$ corresponds to "ordinary" 2D hydrogenic problem), where $\mu$ is the L\'evy index. We show also that in fractional 2D hydrogen atom, the orbital momentum degeneracy is lifted so that its energy starts to depend not only on principal quantum number $n$ but also on orbital $m$. To solve the spectral problem, we pass to the momentum representation, where we apply the variational method. This permits to obtain approximate analytica…