# HW2 - Quantum Mechanics II Physics 4143 Assignment 2 Spring...

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Quantum Mechanics II, Physics 4143: Assignment 2, Spring 2011. 1 : We wish to describe the action of angular momentum operators in a space of ﬁxed angular momentum j = 1. Construct the matrix representations of the operator J x and J y given the following information and using a method similar to that given for j = 1 / 2 in class. Hint : Since j = 1, the dimension of the complex vector space of quantum states is 3 (we call this complex vector space C 3 ). We can represent the normalized basis states (simultaneous eigenvectors of J 2 and J z ) with j = 1 and m = 1 , 0 , - 1, by the column vectors z + = 1 0 0 , z 0 = 0 1 0 and z - = 0 0 1 . You should see by inspection that the action of J 2 and J z on C 3 is represented by the matrices J 2 = 2 ~ 2 1 0 0 0 1 0 0 0 1 and J z = ~ 1 0 0 0 0 0 0 0 - 1 , respectively. 2

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HW2 - Quantum Mechanics II Physics 4143 Assignment 2 Spring...

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