hw1 - 5 '-!. ( a) f h order f irst o rder cor:rectioo c...

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5'-!. (a) fh€ first order corrcctioE is via (5.1.3?) j$st <Olbxl@ = O. th. se.ood order cor:rectioo for tbe €!er8t (c.f. (5.1,42) ad (5.f.43)) ^o= -" l'olt*lol2 - -*z'l'"1*lo'12 ..--t --T-:E- = -o i-E-:E- , r.h.re E! - (r+U/r,. . uo- <alrlo - tfilFld*, sa ^E = -bz (6-/ b,')2/ <1-.o) = -+2 tUu2 ;" the erergy shur, ald tbe coelgy of the g.ou.od state b.coes E(o) td.r + AE = t*u - t2/uo2. (b) Tbe scbrgdingei equatioL for thi-s plobleo is € $fr *1,''2 - 151.o21211, s(o'1 tbat is -I- d'r, 2 -2 ._(o) -2!un21q. EE;2.Irrr r- v (r r o Tbis is agaia a sEo equatior vltb E' = t(o) * u2l2"r2. for losest eaerSy v3fue E' *., u"oc" g(") = ,11, - tz/uuz shi,cb i.s e,.acaty rhe s€se as lbe perturba- tion resulr jn (a). \,2. lrdr (5.L.44) eith k + E ald I +9, ee bave lr, 1r("),* " J, ffi; ......... osrn8 olcbooo-arr. ., o, 1"(o)tt.o ,]"'' .* ,"". Lrlr("$' =' -,2"5.1fE|1-a r ore3r -t2 t2n t , -H H: - (b,z'z + br)t E(o). . Let r' = $b/uoz, thal abqve equatiso ca! be reahceal to lvoL, lL ,l ., +- I\<ttt nu = [.q1 ;11 anLri.,,.i,'; i.;i':i' E""t -\t l +,4wr+td,l ir ,t,i (u ,,,,, h?'.:t"-,1,4f p",tl t'Aet h., aa h*. .t ,, ^tit t-"1 aQ J. -", ba'
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t 3. Sotwtrt lbc Schr8d\pr .qlrslloa fo! tb€ rsFlEulbca .:/taa.' E c.a . .!!lt flld tb€ co.rt c1g.dfroccLo!. . ltrt rrc tc ' {frtt|t, .tfltn .tstlL '}t+"+ fo.
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This note was uploaded on 12/30/2011 for the course PHYSICS 623 taught by Professor Galitski during the Summer '10 term at Maryland.

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hw1 - 5 '-!. ( a) f h order f irst o rder cor:rectioo c...

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