Calculate the angles that the angular momentum vector L can make with the z-axis for l= 1,

Question:

Calculate the angles that the angular momentum vector L can make with the z-axis for l= 1, as illustrated in Figure 30.52.

Strategy

Figure 30.52 represents the vectors Land Lz as usual, with arrows proportional to their magnitudes and pointing in the correct directions. L and Lz form a right triangle, with L being the hypotenuse and Lz the adjacent side. This means that the ratio of Lz to L is the cosine of the angle of interest. We can find L and Lz using L = (1+1) 2x and h m 2x L= m-.z-axis m = 1! L m, 0 L 0 83 m = 0 L

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