Perturbation Theory Eigenvalue Problem - Handwritten Notes | PHYS 6124, Study notes of Physics

Download Perturbation Theory Eigenvalue Problem - Handwritten Notes | PHYS 6124 and more Study notes Physics in PDF only on Docsity! Peetu bation theory foc Eigenvalue Prob Som Met (A+eB) Xp ASS Unpecturdadl pcobhem 3 At. = a:e: Assuming arts non=deqenecake Use Bx Pan sions a 0) z ey) = Spe SKS OF FM t i ~, \ ME a as mee Be Mee ~ 2 (Aseb ee ex; & gv. ~ (a; + exe eek wo) Eee 00 +O XA > >» (0¥ ot eo: A@ = a.e: ( caccect chotee off BP 08 4 1D 2) o> és ASE+ Be, = Apt nee a =O nt et ASR BRP = a: KP EP ney Figet ordee Ge hucbakians Dedine 2a fc LaemsrckOCs : TA =a; Q. - — Note: f, 2, = 5 4RHxt => Normakne GtS= 4 Note: for A- hestinat Syromencce) F, L=O; Taree = FR eg, 7 t > _ eer oY > shh ie eee) = Orlh pe) + 48 ty Solve width seapeck to o foc Jats Let Yes Tea, > FKP. ae aw , a op h. oO Qodvg with cgpeet to a; foc fei: ¢ (E-Bay, Re S Oy 7, Finally obtain oe. ~ a . 4 | Note: pectuc bakvon IE Pansinn dorg wot Pix te vabxof Cp. t Vo make the oloter cg Coun cere GX Pee? = 5 Second ocdec poche batons Se (ART BRP) = t;. (a RPO IOS > -a:) (F994 Ge ex) = NPE K) 408, Vor jai obtain Foo j¥t obtacn (38 (ac-ay\@= — Fee?) 4 Addex?) ce Chad ‘ > ReBE GS) 2 yen ¢ oe e - 2 (Reed Geen K ay . ye a vgiy (TS ENR AG) — ® . ‘ . ce Note i OF is again wadetecmined Cueitrer wilt be @ ’ | Examples, (© e\ fe, ol fo t\ = | ;t ey \ g E, | \o €,] (4 of enn LS A 2 Ao gupnnekic ee = (4) , oar i (2) a \ Birt odels on. ged - 0 ss \ls)~ 9 = Ga Bey ge =~ t@ (ean add a mabtoree of &) Stentor La Od SOs gwap A&e2 A2S Exxoumn a_i 4’ - Ag seps= oO 5 Yyo=yor) Cond hasnt urs Xe) ap te AS* o¢ doe wt Rowt 2 ag oe eee ay Ky Sy Note: the Loc wlas don't change t¥ Woe Sephoeg Sauss —> BCSxe) oh Orda AGRA Bra Ay WRB.C. > ye= ae BR adaanvechors 3 w= oN Dasgnecare re ham Non on oe +l gs + a wa = 4 eA + ite: Qa ft ertyrt ONock acerhe same. (you MR have ho frugk thts) 4 use GOS Bla yess dain > Od) da ol A vets Aas Jake aXe = Pat Sxactin wha we mepucts Dente sy n= Mag tole yO ao Ka22 Blekystelyy)= oats * core ye We ww 2 a7 Bthn Yao => AD= 5 Keone ordre, Yn ola yn) + hn dass KeSi BOdgeeLy) = oe oye 4 Boliol_ ue Ht Boll qe Ye +g Nee re oth gn inx Scat § = sales = ole 2D => Seleel = On” fo) ae nm layin tol Yn day oS Nz on® +38otsl tos G. Rectiux hobton Tory for Dearmecat]e. hatrvess ° (Ate B® = am. = mr 4 EAD ts a . \ (ae® GP Pan) = Kin ROH ELP Hs \ = (B+ EAPO (ROL ERP ES v to) = 1) 2 AQ = 0% . => Wea, expavaat of A, YO — Some eigenaator lich covasponds to ay We howe nok Bokermused Sf te OM ts degenerate Te MD eg. Nekemes degenorabe , on wd, woli@y sic elidy Loeftecramte, oy ase tet Aobecmimad by 0" order equations. Ley oSe dotecnined by higher oder aquattens ' te > > a SC WwW Woy EE DNPH ERD = WON OE ‘ \ at 2 ee Nuttopts by Gi ont a ashe KP \-( freee) @ =a:(B P+ nore a j= Ay eny = Nequadions foc Awervatue corceckeon rn B) jx neh hh > New zawareong fof aigamwchor comeckten we oj! Ryan y= 2k G8) = PE Ge) > Baa Bie 8h te Bits wor-degenarara thos axgonpcoblin Aekecmenes, both aPC 1% ocdee Larm in Ch envatue Sepansion ) and at =Wiy. oh) CO acdor term ta eegenvector Lx pansion) TEE es also dogenoxte, dk waght Cor might not be) derormaned bby Kigher otdecs of peck Nlsomys o3 Exempt ae (SO) a O02 G-d-C), BeG= 0), or =t Ya d+ 25 Be $pB.~ Sp = B ~degenorete / => 4, ol, — ecbetrany » (Cote evartty: Aya (+e Yn w/Free he ¥er,2) Exmptes AR (LP) eo COA) 7 a) % ~ ay z { Be = $5-R =. BR = HP 20 > ABE! —KEN dagen.