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Exercise 5.11 Consider the wave function y (0,0) = 3 sin 0 cos 0e -2(1-cos²0)e²i. (a) Write y(0, 0) in terms of the spherical harmonics. (b) Write the expression found in (a) in terms of the Cartesian coordinates. (c) Is y(0, 0) an eigenstate of 1² or 1₂?

Exercise 5.11 Consider the wave function y (0,0) = 3 sin 0 cos 0e -2(1-cos²0)e²i. (a) Write y(0, 0) in terms of the spherical harmonics. (b) Write the expression found in (a) in terms of the Cartesian coordinates. (c) Is y(0, 0) an eigenstate of 1² or 1₂?

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Exercise 5.11 Consider the wave function y(0,0) = 3 sin cos 0e -2(1-cos²0)e²i (a) Write y(0, 0) in terms of the spherical harmonics. (b) Write the expression found in (a) in terms of the Cartesian coordinates. (c) Is (0, 0) an eigenstate of L² or L₂? (d) Find the probability of measuring 2ħ for the z-component of the orbital angular mon tum.
Transcribed Image Text:Exercise 5.11 Consider the wave function y(0,0) = 3 sin cos 0e -2(1-cos²0)e²i (a) Write y(0, 0) in terms of the spherical harmonics. (b) Write the expression found in (a) in terms of the Cartesian coordinates. (c) Is (0, 0) an eigenstate of L² or L₂? (d) Find the probability of measuring 2ħ for the z-component of the orbital angular mon tum.
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