On a semiclassical formula for non-diagonal matrix elements

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F07%3A04135984" target="_blank" >RIV/68407700:21340/07:04135984 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
On a semiclassical formula for non-diagonal matrix elements
Original language description
Let H (h) = -h^2 d^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 = liminf_{|x| -> infty} V (x). We consider the semiclassical limit n -> infty, h = h_n -> 0 and E_n = E where E_n is the nth eigenenergy of H (h). An asymptotic formula for <n|W (x)|n + k>, the non-diagonal matrix elements of W (x)in the eigenbasis of H (h), has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.
Czech name
Není k dispozici
Czech description
Není k dispozici

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GA201%2F05%2F0857" target="_blank" >GA201/05/0857: Application of algebraical and functional analytical methods in mathematical physics</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2007
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)