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# form108 - z = a ib ei = cos i sin ei =-1 ei 2 = i 1 1 cos...

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e = cos φ + i sin φ e = - 1 e i π 2 = i cos φ = 1 2 ( e + e - ) sin φ = 1 2 i ( e - e - ) z = a + ib z * = a - ib z = ρe z * = ρe - | z | 2 = zz * a, b, ρ, φ are all real. z is complex. μ B = e ¯ h 2 m e = 5 . 8 10 - 5 eV / Tesla ± M spin = - g s μ B ± S ¯ h = γ ± S γ = - g s μ B ¯ h ≈ - 2 e ¯ h 2 m e ¯ h = - e m e 1 eV = 1 . 6 10 - 19 J ¯ hc = 200 eV - nm m e c 2 = 0 . 511 MeV M p c 2 = 940 MeV sin a 2 = q 1 2 (1 - cos a ) cos a 2 = q 1 2 (1 + cos a ) sin 2 a = 2 sin a cos a cos 2 a = cos 2 a - sin 2 a sin( a ± b ) = sin a cos b ± cos a sin b cos( a ± b ) = cos a cos b sin a sin b cos 2 a - sin 2 b = cos( a + b ) cos( a - b ) sin 2 a - sin 2 b = sin( a + b ) sin( a - b ) cos 2 a - cos 2 b = - sin( a + b ) sin( a - b ) Matrix representations of states The eigenstates of S z are | + ² is ˆ 1 0 ! and |-² is ˆ 0 1 ! ³ + | is 1 0 · and ³-| is 0 1 · The eigenstates of S x are | + ² x = 1 2 ( | + ² + |-² ) |-² x = 1 2 ( | + ² - |-² ) 1 2 ˆ 1 1 ! and 1 2 ˆ 1 - 1 ! The eigenstates of S y are | + ² y = 1 2 ( | + ² + i |-² ) |-² y = 1 2 ( | + ² - i |-² ) 1 2 ˆ 1 i ! and 1 2 ˆ 1 - i ! Matrix representations of operators
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