66 citations · 301 across the 16 of their papers we have counts for
5 papers · 1 filter
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…
Solutions for certain classes of Riccati differential equation
Nasser Saad, Richard L Hall, Hakan Ciftci
We derive some analytic closed-form solutions for a class of Riccati equation y'(x)-λ_0(x)y(x)\pm y^2(x)=\pm s_0(x), where λ_0(x), s_0(x) are C^{\infty}-functions. We show that if…
Solutions to the 1d Klein-Gordon equation with cutoff Coulomb potentials
Richard L. Hall
In a recent paper by Barton (J. Phys. A40, 1011 (2007)), the 1-dimensional Klein-Gordon equation was solved analytically for the non-singular Coulomb-like potential V_1(|x|) = -α/(…
Binding energies of semirelativistic N-boson systems
Richard L. Hall, Wolfgang Lucha
General analytic energy bounds are derived for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N \sqrt(p_i^2+m^2) + \sum_{1=i<j}^N V(r_{ij}), whe…
Schroedinger secant lower bounds to semirelativistic eigenvalues
Richard L. Hall, Wolfgang Lucha
It is shown that the ground-state eigenvalue of a semirelativistic Hamiltonian of the form H = sqrt(m^2+p^2) + V is bounded below by the Schroedinger operator m + beta p^2 + V, for…