LEADER 00904cam0 2200289 450 001 E600200060573 005 20201008072534.0 010 $a3525332491 100 $a20100226d1980 |||||ita|0103 ba 101 $ager 102 $aDE 200 1 $aKant$fStephan Körner 205 $a2., unveränderte Auflage 210 $aGöttingen$cVandenhoeck & Ruprecht$d1980 215 $a198 p.$d19 cm 225 2 $aKleine Vandenhoeck-Reihe 410 1$1001LAEC00027183$12001 $a*Kleine Vandenhoeck-Reihe 700 1$aKörner$b, Stefan$3A600200060034$4070$0775427 801 0$aIT$bUNISOB$c20201008$gRICA 850 $aUNISOB 852 $aUNISOB$j100$m70197 912 $aE600200060573 940 $aM 102 Monografia moderna SBN 941 $aM 957 $a100$b007554$gSi$d70197$racquisto$1pregresso2$2UNISOB$3UNISOB$420100226092004.0$520201008072519.0$6Alfano 996 $aKant$91704131 997 $aUNISOB LEADER 03536nam 22006855 450 001 9910299770303321 005 20220426233942.0 010 $a4-431-55702-4 024 7 $a10.1007/978-4-431-55702-9 035 $a(CKB)3710000000444539 035 $a(EBL)3567544 035 $a(SSID)ssj0001534899 035 $a(PQKBManifestationID)11856008 035 $a(PQKBTitleCode)TC0001534899 035 $a(PQKBWorkID)11497729 035 $a(PQKB)10390972 035 $a(DE-He213)978-4-431-55702-9 035 $a(MiAaPQ)EBC3567544 035 $a(PPN)187687838 035 $a(EXLCZ)993710000000444539 100 $a20150707d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aVirtual turning points /$fby Naofumi Honda, Takahiro Kawai, Yoshitsugu Takei 205 $a1st ed. 2015. 210 1$aTokyo :$cSpringer Japan :$cImprint: Springer,$d2015. 215 $a1 online resource (133 p.) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v4 300 $aDescription based upon print version of record. 311 $a4-431-55701-6 320 $aIncludes bibliographical references and index. 327 $a1. Definition and basic properties of virtual turning Points -- 2. Application to the Noumi-Yamada system with a large Parameter -- 3. Exact WKB analysis of non-adiabatic transition problems for 3-levels -- A. Integral representation of solutions and the Borel resummed WKBsolutions. 330 $aThe discovery of a virtual turning point truly is a breakthrough in WKB analysis of higher order differential equations. This monograph expounds the core part of its theory together with its application to the analysis of higher order Painlevé equations of the Noumi?Yamada type and to the analysis of non-adiabatic transition probability problems in three levels. As M.V. Fedoryuk once lamented, global asymptotic analysis of higher order differential equations had been thought to be impossible to construct. In 1982, however, H.L. Berk, W.M. Nevins, and K.V. Roberts published a remarkable paper in the Journal of Mathematical Physics indicating that the traditional Stokes geometry cannot globally describe the Stokes phenomena of solutions of higher order equations; a new Stokes curve is necessary. 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v4 606 $aMathematical physics 606 $aDifferential equations 606 $aQuantum theory 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 615 0$aMathematical physics. 615 0$aDifferential equations. 615 0$aQuantum theory. 615 14$aMathematical Physics. 615 24$aOrdinary Differential Equations. 615 24$aQuantum Physics. 676 $a515.353 700 $aHonda$b Naofumi$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755709 702 $aKawai$b Takahiro$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTakei$b Yoshitsugu$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299770303321 996 $aVirtual Turning Points$92544374 997 $aUNINA