Word Count : 472

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We are asked to write down the eigenkets (|j, m_j\rangle) for (j = j_1 + j_2) with (j_1 = 2) and (j_2 = \frac{1}{2}). Let's solve this step by step numerically, without using any programming tools. --- Step 1: Determine the possible values of (j) For the addition of angular momenta (j_1) and (j_2): [ j = j_1 + j_2, j_1 + j_2 - 1, \dots, |j_1 - j_2| ] Here, (j_1 = 2) and (j_2 = \frac{1}{2}), so [ j_{\max} = j_1 + j_2 = 2 + \frac{1}{2} = \frac{5}{2}, \quad j_{\min} = |2 - \frac{1}{2}| = \frac{3}{2} ] Thus, the possible (j)-values are: [ j = \frac{5}{2}, \frac{3}{2} ] --- Step 2: Identify the corresponding (m_j) __________ ___ _________ _______ ______.
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