caa a22 4500 463196929 CHVBK 20180406164925.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s10773-006-9249-2 doi (NATIONALLICENCE)springer-10.1007/s10773-006-9249-2 Multidimensional WKB Approximation for Tunneling Along Curved Escape Paths [Elektronische Daten] [J. Zamastil, L. Skála] Asymptotics of the perturbation series for the ground state energy of the coupled anharmonic oscillators for the positive coupling constant is related to the lifetime of the quasistationary states for the negative coupling constant. The latter is determined by means of the multidimensional WKB approximation for tunneling along curved escape paths. General method for obtaining such approximation is described. The cartesian coordinates (x,y) are choosen in such a way that the x-axis has the direction of the probability flux at large distances from the well. The WKB wave function is then obtained by the simultaneous expansion of the wave function in the coordinate y and the parameter γ determining the curvature of the escape path. It is argued, both physically and mathematically, that these two expansions are mutually consistent. Several simplifications in the integrations of equations are pointed out. It is shown that to calculate outgoing probability flux it is not necessary to deal with inadequacy of the WKB approximation at the classical turning point. The WKB formulas for the large-order behavior of the perturbation series are compared with numerical results and an excellent agreement between the two is found. Springer Science+Business Media, LLC, 2007 multidimensional wkb approximation nationallicence large-order behavior of the perturbation series nationallicence Zamastil J. Department of Chemical Physics and Optics, Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2, Prague, Czech Republic aut Skála L. Department of Applied Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut International Journal of Theoretical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 46/4(2007-04-01), 898-919 0020-7748 46:4<898 2007 46 10773 https://doi.org/10.1007/s10773-006-9249-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-006-9249-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zamastil J. Department of Chemical Physics and Optics, Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2, Prague, Czech Republic aut NATIONALLICENCE 700 1- Skála L. Department of Applied Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 46/4(2007-04-01), 898-919 0020-7748 46:4<898 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer