On a semiclassical formula for non-diagonal matrix elements
| dc.creator | Lev, O. | |
| dc.creator | Stovicek, P. | |
| dc.date | 2006-11-09 | |
| dc.date.accessioned | 2026-07-07T11:23:04Z | |
| dc.date.available | 2026-07-07T11:23:04Z | |
| dc.description | Let $H(\hbar)=-\hbar^2d^2/dx^2+V(x)$ be a Schrödinger operator on the real line, $W(x)$ be a bounded observable depending only on the coordinate and $k$ be a fixed integer. Suppose that an energy level $E$ intersects the potential $V(x)$ in exactly two turning points and lies below $V_\infty=\liminf_{|x|\to\infty} V(x)$. We consider the semiclassical limit $n\to\infty$, $\hbar=\hbar_n\to0$ and $E_n=E$ where $E_n$ is the $n$th eigen-energy of $H(\hbar)$. An asymptotic formula for $<{}n|W(x)|n+k>$, the non-diagonal matrix elements of $W(x)$ in the eigenbasis of $H(\hbar)$, has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner. | |
| dc.description | LaTeX2e | |
| dc.identifier | https://arxiv.org/abs/hep-th/0611109 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0611109 | |
| dc.identifier | Int.J.Theor.Phys.46:2688-2707,2007 | |
| dc.identifier | doi:10.1007/s10773-007-9382-6 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/194776 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | On a semiclassical formula for non-diagonal matrix elements | |
| dc.type | text |