Question

Given: A = AJ + B ↑ + C hz and the following commutation relations [ Ix, Jy ] = ih ] , [ I ] ] = {ħ fx, [ fz , ] ]=- iħ ly a) As briefly as possible show it is possible that eigen functions cand b can be given as: (=t? JCJ+1); b= ħk where r = 0, +1, +2.. IJON L J2Y = (YK ₂ Y J K = by se b) if A=B & G show that is an eigen function of Ĥ with eigenvalves : Esk = ?[OJC5+) +CC-B)k?]

please answer the question FULLY and clearly for a thumbs up

Answer 1

4iven thar 7-J = 1,-1 tz . ,) F1J=-243

ince, |フラフ2]=0 . ) +ら Poroible to 04tain m tancous eisanvestons toa these to opamatops Let くけ): ()+くう) 大くス) うCこく)+くッ>+と 76 94he amallest vakue ot e be ,16m = 3 Amax

1 me -> mklim) Eigenstakes 1 m) ape ontenownalizas Kim1im)-S JJ=- = t(m-1) 1113 m) m3) 7_ li m Il 115 m)=F

, j tate can't est C=0-.if+ j(j-ハ大 b= 大k Clearly, 1ou have considered Sridered 1Je, 7,> it and ealedato wo ald veruAn

H3E = E.Y. 1K B (Jt Ci)ia B

Lad eoside ras +hen, 2 1.15 ) C 21 )C_ li m

) +6 7, l5 1) +71s 3) C-OTTO. j i mar3 ..