The one-dimensional Schrödinger-Newton equations
We prove an existence and uniqueness result for ground states of one-dimensional Schrödinger-Newton equations.
math-ph↗
arXiv subjects
J. Stubbe
Publications and source records attributed to J. Stubbe.
Asymptotic properties of the solutions of a differential equation appearing in QCD
We establish the asymptotic behaviour of the ratio $h^\prime(0)/h(0)$ for $λ\rightarrow\infty$, where $h(r)$ is a solution, vanishing at infinity, of the differential equation $h^{\prime\prime}(r) = iλω(r) h(r)$ on the domain $0 \leq r <\infty$ and $ω(r) = (1-\sqrt{r} K_1(\sqrt{r}))/r$. Some results are valid for more general $ω$'s.
hep-th↗
Generalization of the Calogero-Cohn Bound on the Number of Bound States
It is shown that for the Calogero-Cohn type upper bounds on the number of bound states of a negative spherically symmetric potential $V(r)$, in each angular momentum state, that is, bounds containing only the integral $\int^\infty_0 |V(r)|^{1/2}dr$, the condition $V'(r) \geq 0$ is not necessary, and can be replaced by the less stringent condition $(d/dr)[r^{1-2p}(-V)^{1-p}] \leq 0, 1/2 \leq p < 1$, which allows oscillations in the potential. The constants in the bounds are accordingly modified, depend on $p$ and $\ell$, and tend to the standard value for $p = 1/2$.
hep-th↗