Exercise 5.10 Consider the operator  = ½ (ĴxĴy + ĴyĴx). (a) Calculate the expectation value of  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.
Exercise 5.10 Consider the operator  = ½ (ĴxĴy + ĴyĴx). (a) Calculate the expectation value of  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.
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Transcribed Image Text:Exercise 5.10
Consider the operator  = ¹(ĴxĴy + ĴyĴx).
(a) Calculate the expectation value of  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 5.11
Consider the wave function
y (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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