Chapter 10 Lecture

Chapter 10 Lecture - Chapter 10- Spin 10-1 In 1922 Stern...

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Chapter 10- Spin 10-1 In 1922 Stern and Gerlach discovered that atoms in an L=0 state could be split in to two groups when passed through a magnetic field with a gradient. Let B = 0 , B 0 , dB dz z ! " # $ % ! μ = e ! L 2 m magnetic moment of a circulating ch arg e E = ! i ! B energy of a dipole in a B field ! F = ’( ! i ! B ( ) = ! ( x B x + y B 0 + z dB dz z ! " # $ % = 0, 0, z dB dz ! " # $ % ) Z = 1 2 at 2 = 1 2 e 2 m e dB dz ! " # $ % " 2 v 2 L Z Deflection corresponded to L Z = # $ 2 and int rinsic spin was dis cov ered ! In general the relation can be written ! S = g e 2 m e ! S g = gyromagnetic ratio ! 2.0 10-2 Spin Operators and Algebra S I , S J ! " # $ = i ! S K % IJK antisymmetric a lg ebra S 2 , S I ! " # $ = 0 i = 1,2,3 S 2 commutes with S X , S Y , S Z S 2 | s , ± m s >= s ( s + 1) ! 2 | s , ± m s > S Z | s , ± m s >= ± ! m s ! | s , ± m s > s = 1 2 , m s = ± 1 2 S 2 1/ 2, ± 1/ 2 = 3 4 ! 2 1/ 2, ± 1/ 2 S Z 1/ 2, ± 1/ 2 = ± 1 2 ! 1/ 2, ± 1/ 2 10-2 Matrix Representation S=1/2 S 2 = 3 4 !
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Chapter 10 Lecture - Chapter 10- Spin 10-1 In 1922 Stern...

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