Exercise 5.10Consider the operator Â = ¹(ĴxĴy + ĴyĴx).(a) Calculate the expectation value of Â and A with respect to the state | j, m).2(b) Use the result of (a) to find an expression for A² in terms of: Ĵ4, 3², 3², Ĵ4, Ĵª.Exercise 5.11Consider the wave functiony (0, 9) = 3 sin cosei - 2(1-cos²0)e²i(a) Write y (0, p) in terms of the spherical harmonics.(b) Write the expression found in (a) in terms of the Cartesian coordinates.(c) Is y (0, p) an eigenstate of 1² or 1₂?(d) Find the probability of measuring 2ħ for the z-component of the orbital angular momen-tum.

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Answered: Exercise 5.10 Consider the operator Â =…

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Exercise 5.10 Consider the operator Â = ½ (ĴxĴy + ĴyĴx). (a) Calculate the expectation value of Â and Ẩ² with respect to the state | j, m). (b) Use the result of (a) to find an expression for A² in terms of: Ĵ4, Ĵ², 3², ĴĄ, Ĵª.