《wkb方法介绍》PPT课件.ppt
WKBReadingMaterials:曾谨言,量子力学(IID)第三版,2.4苏铷铿,量子力学TheWKBapPproimation卵US.itsWKBentzdKramersBnloaimHialanditsKWB卵HrameeitsBWK卵EnglanditsIVKB(orleilesyItsprincipalapplicationsforusw议beincaleulatingbound-stateenergiesandtunnelingratesthroughpotentialbarriers:.1.Classicalegion(E>工)w=-with大世朋n五一历T3么_厂-一L|一2.Nonclassicalregion(E<左)l一命自一-(tunnslingregion)下一5reoWCJ=derwithx万y2(P一五庆+(KE.+PE)3.Tumingpoint(E工左)ClassicalregionTheSchridingerequation4Cn:amplitudIngeneral:y二4GOJere,岫盯e哥CDampatde因LbCo:phaseSabstituting(2)into(1),万WKBmethods丁十2什8十同br一4(97一一技廷Jismnotacomstantbutinsteadvaricsyeryslowlyonadistncescaleof.thenitisreasonable(4ib)=0tosopposethatenainspracticaliysinusoidaL心cxeeptthatthewavelmgthandanpliudechangc一4荻蹴一-slowlywtthx不-an亚一分=Beth(6Jand关Puttingthesolationsto(2)xExampleforClassicalregion1YC9=aCoe抨痘-目荨u、扁Cs】n纹、一Ccos纹、m山叭U一一jp)somespeeiedfimnetion.诉0<x<aothervisc心1“LL'/】二sab(g=0二blal<nz(-二n广pCOde-IDnE-rtol|忡f(_-六心1歪PC9=0at0<x<a二pa=nnputtingthesoltonsto(3)(4)vExample,potentialforharmonicoscillator,howabouttheenergyforthissystem2厂(=壹AorxeThecoordinateofTurningpoints:量m镳z二E斗x=J2E1eorie.5二-a=V21eo7。1心囝婀庄一zI履PQx二2/ZE/m一("十三)/z1E=(+二)方(z)Keepingthesamedefinitionofp(x).ifisnow|motrealbutimaginary.Asimilarsetofnmanipulationsleadstothesolution:|Nonclassical(tunnelin不|yGo区ExampleAtx<0:9d小B一wbth人世s口Atxr>a:VC9=Fe*Attunclingregion(0Sx<ak矗TransmissionpmbabittyGamowstheoryofalphadecaywcouonbepssenAnalphepertcleconain-Tvoprotons&neuronsIuclearforceETepulsiveelectriceforce=198MEV“2尿n怡一区eomDearIogt1AvermgevelocityofalphaparticlevAvermgetmebetween“collsionswiththewallFrequencyofcollisions二ETheprababitityofescape.perunittime:崇一hThelifetmeoftheparentmucleusE目D二DT7=5xI0TEnote:AE=1MaV=9.7x109InolTheconnectionformulasUDnestzedpoeriaWKBapproximation:forClassicalregion1簪姜e熹上,十Be穴I8-让x<0二Y=.【C兵J剽浠叮厂Deifeeoleifx>0Ipcol讨x一0斗p(X)与J2m万一(x)一0斗y(x)一05驭r、|【YCO=e口forNonclassicalregion-eee|pGol一sasarnagonnagoniT辜pon丨蓁Uneatzedpoerta9PatchingwavefunctionP(g东E+T(O)x万a+Bx|straightlineequationDirectlysolvedbytheSchrodingereqation:汀+E+厂(0Jxy二y门一【z二3271,“命院E邸赘0xyo:Wherey(0)217Casseal0Nonstssecal“letz井magonnagonet=三rQE鲨二zY。.AirysequationSolutions之M=adi(za)+DBi(:)