1 Cartesian Components Of S For Spin Recall That Any Operator A Can Expanded In Its Own Basis As A En Anlanan Where 1 (18.86 KiB) Viewed 115 times
Quantum Mechanics
1. Cartesian components of S for spin-. Recall that any operator A can expanded in its own basis as A = En anlanan where lan) are the eigenkets of A belonging to eigenvalues an. Verify the following by explicit calculation using and |±)x= 士x = 1 + ) ± √ √/2/21-) |t)y = 1 |+) ± i. Sx = {1+X-1 + 1-X+1} = 0₁ ii. Sy = {-i|+X-1 + il-X(+1} = 10₂ iii. S² = S² + S² + S² = ²h²1 = ² n² (²9) where 1 is the identity operator.
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