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Determine all possible projections onto the z-axis and the x-y plane of the total angular momentum vector where L² = 1(1 + 1) and let l = 1. While we know the magnitude of the angular momentum and its z-components, we do not know the direction in which the vector Îx + Îy points. Why is this so and to what region of space can it be known? (Hint: it might help to draw a picture).

Determine all possible projections onto the z-axis and the x-y plane of the total angular momentum vector where L² = 1(1 + 1) and let l = 1. While we know the magnitude of the angular momentum and its z-components, we do not know the direction in which the vector Îx + Îy points. Why is this so and to what region of space can it be known? (Hint: it might help to draw a picture).

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(a) Determine all possible projections onto the z-axis and the x-y plane of the total angular momentum vector where \(L^2 = l(l+1)\) and let \(l = 1\). (b) While we know the magnitude of the angular momentum and its z-components, we do not know the direction in which the vector \(\hat{L}_x + \hat{L}_y\) points. Why is this so and to what region of space can it be known? (Hint: it might help to draw a picture).
Transcribed Image Text:(a) Determine all possible projections onto the z-axis and the x-y plane of the total angular momentum vector where \(L^2 = l(l+1)\) and let \(l = 1\). (b) While we know the magnitude of the angular momentum and its z-components, we do not know the direction in which the vector \(\hat{L}_x + \hat{L}_y\) points. Why is this so and to what region of space can it be known? (Hint: it might help to draw a picture).
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