Consider two spin 1/2 particles and define the operator S₁2 =B (S₁ S₂), B is a constant. . B (a) Use the spin raising an

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Consider Two Spin 1 2 Particles And Define The Operator S 2 B S S B Is A Constant B A Use The Spin Raising An 1 (61.76 KiB) Viewed 5 times

Consider two spin 1/2 particles and define the operator S₁2 =B (S₁ S₂), B is a constant. . B (a) Use the spin raising and spin lowering operators to show that S₁2= S₁ S₂ + S₁ S₂ + B S₁₂ S₁₂ 1+ 2- (b) Calculate: (b1) S₁2 xx (b2) S12 xx (3) S12 xx (b4) S₁2 X¹ X² (c) Construct the 4x4 matrix corresponding to the operator S12 (option A). (d)| Use S=S₁+S₂ and show that S₁2=-B S²-S² – S² - 1 1 1 1 (el) Calculate S₁2 12-12-11) 1,1) S12 -,1,0 S12 ,1,- S12 (e2) Construct the 4x4 (e) 2 matrix of S₁ using the eigenkets of option B. Useful formulas and hints S =S₂+iSS=S-iS, Option B: S₁,S₂, s, m.) y