Positive singular radial entire solutions of a biharmonic equation with subcritical exponent are obtained via the entire radial solutions of the equation with supercritical exponent and the Kelvin transformation. The expansions of such singular radial solutions at the singular point 0 are presented. Using these singular radial entire solutions, we construct solutions with a prescribed singular ...

It was shown that the Runge-Lenz vector for a hydrogen atom is equivalent to the raising and lowering operators derived from the factorization of radial Schrödinger equation. Similar situation exists for an isotropic harmonic oscillator. It seems that there may exist intimate relation between the closeness of classical orbits and the factorization of radial Schrödinger equation. Some discussion...

Abstract We study a massless scalar field propagating in the background of a five-dimensional rotating black hole. We showed that in the Myers-Perry metric describing such a black hole the massless field equation allows the separation of variables. The obtained angular equation is a generalization of the equation for spheroidal functions. The radial equation is similar to the radial Teukolsky e...

In this note, we discuss the choice of radial grid in numerical resolution Schroedinger equation. We detail transformation equation resulting from a change variable and function for generic grid, using either explicit or implicit form relation describing variable, apply it to $a r + b \ln(r)$ log-linear mesh. It is shown that, former case, first three derivatives Lambert $W$ are required. This ...