caa a22 4500 463197879 CHVBK 20180406164927.0 cr unu---uuuuu 170326e20071101xx s 000 0 eng 10.1007/s10773-007-9382-6 doi (NATIONALLICENCE)springer-10.1007/s10773-007-9382-6 On a Semiclassical Formula for Non-Diagonal Matrix Elements [Elektronische Daten] [O. Lev, P. Šťovíček] Let H(ℏ)=−ℏ 2d2/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 ∞=lim inf |x|→∞ V(x). We consider the semiclassical limit n→∞, ℏ=ℏ n →0 and E n =E where E n is the nth eigenenergy of H(ℏ). An asymptotic formula for 〈n|W(x)|n+k〉, the non-diagonal matrix elements of W(x) in the eigenbasis of H(ℏ), has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner. Springer Science+Business Media, LLC, 2007 Semiclassical limit nationallicence Non-diagonal matrix elements nationallicence WKB method nationallicence Lev O. Department of Mathematics, Faculty of Nuclear Science, Czech Technical University, Trojanova 13, 120 00, Prague, Czech Republic aut Šťovíček P. Department of Mathematics, Faculty of Nuclear Science, Czech Technical University, Trojanova 13, 120 00, Prague, Czech Republic aut International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/11(2007-11-01), 2688-2707 0020-7748 46:11<2688 2007 46 10773 https://doi.org/10.1007/s10773-007-9382-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-007-9382-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lev O. Department of Mathematics, Faculty of Nuclear Science, Czech Technical University, Trojanova 13, 120 00, Prague, Czech Republic aut NATIONALLICENCE 700 1- Šťovíček P. Department of Mathematics, Faculty of Nuclear Science, Czech Technical University, Trojanova 13, 120 00, Prague, Czech Republic aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/11(2007-11-01), 2688-2707 0020-7748 46:11<2688 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer