## Answers

page:01 Answer We have to consider ah = Rip since loom> -> stationary stałe .. <B>=0 for any a By using Charenfest's theorem we have to show that <T> = (-1/2) (V) The flamillonian is H - E t v (R:) T (Ri) jil am PERP - ERA PE (given) The commutator of H with us is [Hi Re Pi] = R {H, P₂] + [4, Ri] Pi standard commutation sielations are [Hp, D = vitet og and [H, R:) --it Pie ... By using this we get

dv r H, Ri Pi] = iħ ki dr.

It page: 02 Pi m and 7 la in L dRi am (=1 Kinetic energy is Ti - Pape Sind nie, ms are eigen states of both Hand 12 [H,2] 3 ( H, Ri pë] =0 ΣΓΗ CRidv-app 7.0 But T FC kinetic enero » [H, 123 = *ZRead mit 7 From Esthemenfest theorem we have <R>- <[He 2]> But if <R>=0 i=1

pag 03 3 W since in em> are stationary state ' > <[H, 12 ) =0, <[H, 2) >=0 >> { creates -Q<T>=0 ) Qctx = <re Boul Re ( Rv) - Perth The term at the (Rev) > is Sa ei pea (RV 430B3 Sa EP, Vp xor) The boundary condition on y is such that 4 vanishes at the boundaries a and -a - ¿d (Rev)=0 and driver . dR2 ... we are left with DcT>--<v> <T>-- <v> a to visual Theorem

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