Exact, E=0, Solutions for General Power-Law Potentials. II. Quantum Wave Functions
| dc.creator | Daboul, Jamil | |
| dc.creator | Nieto, Michael Martin | |
| dc.date | 1994-08-09 | |
| dc.date.accessioned | 2026-07-07T04:20:25Z | |
| dc.date.available | 2026-07-07T04:20:25Z | |
| dc.description | For zero energy, $E=0$, we derive exact, quantum solutions for {\it all} power-law potentials, $V(r) = -γ/r^ν$, with $γ> 0$ and $-\infty < ν< \infty$. The solutions are, in general, Bessel functions of powers of $r$. For $ν> 2$ and $l \ge 1$ the solutions are normalizable; they correspond to states which are bound by the angular-momentum barrier. Surprisingly, the solutions for $ν< -2$ are also normalizable, They are discrete states but do not correspond to bound states. For $2> ν\geq -2$ the states are unnormalizable continuum states. The $ν=2$ solutions are also unnormalizable, but are exceptional solutions. Finally, we find that by increasing the dimension of the \seq beyond 4 an effective centrifugal barrier is created, due solely to the extra dimensions, which is enough to cause binding. Thus, if $D>4$, there are $E=0$ bound states for $ν> 2$ even for $l=0$. We discuss the physics of the above solutions are compare them to the classical solutions of the preceding paper. | |
| dc.description | LaTeX, 19 pages, preprint LA-UR-94-2569 | |
| dc.identifier | https://arxiv.org/abs/hep-th/9408058 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9408058 | |
| dc.identifier | Int.J.Mod.Phys. A11 (1996) 180 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/53943 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Exact, E=0, Solutions for General Power-Law Potentials. II. Quantum Wave Functions | |
| dc.type | text |