Multiparametric oscillator Hamiltonians with exact bound states in infinite-dimensional space
| dc.creator | Znojil, Miloslav | |
| dc.date | 2003-04-27 | |
| dc.date | 2004-03-08 | |
| dc.date.accessioned | 2026-07-07T06:06:38Z | |
| dc.date.available | 2026-07-07T06:06:38Z | |
| dc.description | Central D-dimensional Hamiltonians $H = p^2 + a |\vec{r}|^2 + b |\vec{r}|^4 + >... + z |\vec{r}|^{4q+2}$ (where z=1) are considered in the limit $D \to \infty$ where numerical experiments revealed recently a new class of q-parametric quasi-exact solutions at $q \leq 5$. We show how a systematic construction of these "privileged" exact bound states may be extended to much higher q (meaning an enhanced flexibility of the shape of the force) at a cost of narrowing the set of wavefunctions (with degree N restricted to the first few non-negative integers). At q=4K+3 we conjecture the validity of a closed formula for the N=3 solutions at all K. | |
| dc.description | 15 pp incl. 4 tables, presented during 24th Winter School ``Geometry and physics" (Srni, Czech Republic, Januar 17 - 24, 2004) | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0304170 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0304170 | |
| dc.identifier | Rendiconti del Circolo Matematico di Palermo, Ser. II, Suppl. 75 (2005) 333-346. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/91047 | |
| dc.subject | Quantum Physics | |
| dc.title | Multiparametric oscillator Hamiltonians with exact bound states in infinite-dimensional space | |
| dc.type | text |