Midterm solution for Quantum Mechanics 2 2018, Study notes of Quantum Mechanics

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Midterm Solutions S//20/6 i. cay CL, hd= cL, Lil RA = 0G, 01+ ly Syke is anti- symmetric in f Re Speke Ea CL La + La Lj) is_symmetric in ¢.R. Asa result, EL*, Lil=o Cl2,l+J= Cle, betelyt = inly rele = 4 Taking the Hermitian conjugate, we have NA A a A “A Cl, laJ=#L 3 Che, LI=-hL C22 Til =o = cL*® T+I=0 @ La (L+/eB>)= (C7, 1+ Z) up> = FGlup>+ BCplup>d = (@tk) (Ble a>)> Ph mpr= orl GIt+ GL) lxp> = Telilyp> = & CG le 2>) (c) Assuming were iS no degeneracy, we. have Lr, B> = C+ (ol B) = Wt Bt >. Simi2orky L-1h8> = CCB) /& B-h> (ZL lees)t = <0 @(Z = [C+r@pl = = = <“@/ Lis +eCG, Gil |~2> =<0w6/2>+-~ZGlee> = &-BEBtI) zo