19 citations · 68 across the 9 of their papers we have counts for
9 papers
New stationary solutions of the cubic nonlinear Schrödinger equations for Bose-Einstein condensates
Qutaibeh D. Katatbeh, Dimitris M. Christodoulou
We have previously formulated a simple criterion for deducing the intervals of oscillations in the solutions of second-order linear homogeneous differential equations. In this work…
Eigenvalue bounds for polynomial central potentials in d dimensions
Qutaibeh D. Katatbeh, Richard L. Hall, Nasser Saad
If a single particle obeys non-relativistic QM in R^d and has the Hamiltonian H = - Delta + f(r), where f(r)=sum_{i = 1}^{k}a_ir^{q_i}, 2\leq q_i < q_{i+1}, a_i \geq 0$, then the e…
Study of anharmonic singular potentials
Nasser Saad, Richard L. Hall, Qutaibeh D. Katatbeh
A simple and efficient variational method is introduced to accelerate the convergence of the eigenenergy computations for a Hamiltonian H with singular potentials. Closed-form anal…
A basis for variational calculations in d dimensions
Richard L. Hall, Qutaibeh D. Katatbeh, Nasser Saad
In this paper we derive expressions for matrix elements (ϕ_i,Hϕ_j) for the Hamiltonian H=-Δ+\sum_q a(q)r^q in d > 1 dimensions. The basis functions in each angular momentum subspac…
Semiclassical energy formulas for power-law and log potentials in quantum mechanics
Richard L. Hall, Qutaibeh D. Katatbeh
We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N =…
Coulomb plus power-law potentials in quantum mechanics
Haken Ciftci, Richard L. Hall, Qutaibeh D. Katatbeh
We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q > -2 and q \ne 0. We show…