Question

Example: Consider a system consisting of two son 1/2 particles and whose Hamiltonian is given by H- A 15.3) + (Seat Sum where A and B are constants having the dimensions of a) Determine the possible son states in coupled and un coupled representations b) which representation is suitable to calculate the expennelues of H? c) Find the energy eipenvalues and their corresponding spin! eigenstates.

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Answer 1

= %== S= 19 - A) 41 马,十 )= 0.1 For Szo mgo Shale 10,0) Jas, moim For S-1, my = +1, 0, -, altone - 1,9,1,1), 11-1) 6 11) = 1 ;告片)1) mon = 1), 1}", ") Appling lowering operator - 1, 1) = (D. - -)/士;士,j) 4] ipatrl+y): - 1 ;士,告》 + J. 1岁,于;士 〉 x 19:古」居中)-4+1,+5:14) + + a)/4+-N) ::::-) | 19 = = ) + G;;;; | = T14:3); }) + 1 +14,47 | 15: [U)17) + 1)}) ] (Symmenie) T. 1 ) - - + J - 每上,士;当!) + 14:45:41 nt F105/1-4) = (T-13,士;子,4》 - -14 3-4) | + 5.古人士)+ 3-4,4;子,士》) ADE 11-1 = 「一+++y/;一号,4) + -r) ; }) +¥17-11-3/4) 1 x 11-1) 士] 1-1) - 去了? //分;; 》7

| my = aj士;;一) + 15·女士,士) <0.01) = 0 a{士,j; k:- ) | + b〈,士;上:上子女,4)=6 a+b=0 - D a -b Joobe) = ) la) +1 4F = ) 10) + b = ) 2012 - lar /> 定 lo, y = =),生;与“士) - 1/4;子,427 ·专广片/413号) - 4,4)) 47 - 完工 17 11) - 12/12] 。 (Antigmeb'c) s

Note coupled basit - Oncoupled basis. Goodluck Page No Date los coupled bess 18 m) 11,-1), 11) Uncoupled basis . =) It, t, 11, 12 181192) 11, 2 + Coupled basis. 18, 88m.) -14) - op 18,8,897) EMS when dr n +822 8 = 8 + 4 = 32 = 8,2 4 8 2 2 + 28 kr 5.81 = 7 1 82-8,2 - 12) h = 15:BL) + (+$27) energy , E = {41874) , 28,8,87|152_3-8097| Bifrlm) + 28,815, m Tis 158,8 m) - the 818+) -4, (8,4) – 197 Xaxtl}ers, small 5,828m) + m2 +278, 8, 8. marts, esm) ER ( 8C8+11 – 28, CRP)] + Bm? 964 8, 82

Good Luck Page No. © Date ,147=14,; 1,1) Goodluck para be 1?(14) 2X 115 ed] + B1032 14)_115, 1,0) y E A [1 (141) - 2x21 2 ] + Blo2 = A 11141) - 2x2 (2+1)] +B (-12 147 = ty - titi 0,0) Oleu - 2x12 (beo] estuje