5. Spin states and uncertainty [25 points] (a) Derive an uncertainty relation for the S, and S, operators. That is, given a state ), demonstrate an inequality of the form (AST) (AS) .... where the right-hand side is a function of 4). (b) What is the minimum possible value of the product ASAS,? For which states ) is this minimum achieved? (c) What is the maximum possible value of AS, for any i = 1,2,3? Explain. (d) Consider a general spin state n;+) described in terms of the angles and o. Calculate AS, AS, and AS. Based on your result, what are the states that maximize the product AS, AS? Explain.