ECE453Fall2010HW9[1]

# ECE453Fall2010HW9[1] - Fall 2010 HW # 9 ECE 453 HW #9 Due...

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Fall 2010 ECE 453 HW #9 Due 12/6 (Monday) HW # 9 Due Monday, December 6, 2010 These problems are based on Chapters 19, 20 of notes (see Notes#6). This is the last Home Work for the semester. Pauli spin matrices: (2x2) Identity matrix: ! x = 0 1 1 0 " # \$ % , y = 0 " i + i 0 # \$ % ( , z = 1 0 0 " 1 # \$ % ( I = 1 0 0 1 ! " # \$ % [ ! . ! V 1 ] [ ! . ! V 2 ] = ( ! V 1 . ! V 2 ) [ I ] + i [ ! .( ! V 1 " ! V 2 ) 1. What are the eigenvalues of the (2x2) matrix ! . ˆ n " x sin # cos \$ + y sin sin + z cos Show that the corresponding eigenvectors can be written as c s ! " # \$ % , ! s * c * " # \$ % , where c ! cos " 2 e # i /2 , s ! sin 2 e + i / 2 2. Consider a device with two spin-degenerate levels described by [ H ] = 0 0 " # \$ % . It is connected to four magnetic contacts with one pointing along + ˆ z and one along ! ˆ z described by [ ! 1 ] = " i 2 0 0 % ( ) * , [ ! 2

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## ECE453Fall2010HW9[1] - Fall 2010 HW # 9 ECE 453 HW #9 Due...

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