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48 Physics Formulary by ir. J.C.A. Wevers 10.10 Spin For the spin operators are defned by their commutation relations: [ S x ,S y ]= i ¯ hS z . Because the spin operators do not act in the physical space ( x, y, z ) the uniqueness o± the wave±unction is not a criterium here: also hal± odd-integer values are allowed ±or the spin. Because [ L,S ]=0 spin and angular momentum operators do not have a common set o± eigen±unctions. The spin operators are given by ± ± S = 1 2 ¯ h ± ±σ , with ± x = ± 01 10 ² , ± y = ± 0 - i i 0 ² , ± z = ± 0 - 1 ² The eigenstates o± S z are called spinors : χ = α + χ + + α - χ - , where χ + =(1 , 0) represents the state with spin up ( S z = 1 2 ¯ h ) and χ - =(0 , 1) represents the state with spin down ( S z = - 1 2 ¯ h ). Then the probability to fnd spin up a±ter a measurement is given by | α + | 2 and the chance to fnd spin down is given by | α - | 2 . O± course holds | α + | 2 + | α - | 2 =1 . The electron will have an intrinsic magnetic dipole moment ± M due to its spin, given by ± M = - eg S ± S/ 2 m , with g S =2(1+ α / 2 π + ··· ) the gyromagnetic ratio. In the presence o± an external magnetic feld this gives
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This note was uploaded on 01/30/2011 for the course PHYSICS 208 taught by Professor Ye during the Spring '10 term at Blinn College.

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