4. If an atom is not in a magnetic field or other probe of its angular momentum direction, then it is equally likely to be found in any allowed state of L̟. For the p state, this means that it can be represented by a superposition of states 1 Y (8.6) = Y1. Y1,-1 + Y10 + V3 %3D Y11 (a) Show that in this case, the overall probability density |Y (0,0)|² = Y* (0,6) Y (8, ø) is independent of both 0 and ø.? (b) Show explicitly that it is properly normalized.
4. If an atom is not in a magnetic field or other probe of its angular momentum direction, then it is equally likely to be found in any allowed state of L̟. For the p state, this means that it can be represented by a superposition of states 1 Y (8.6) = Y1. Y1,-1 + Y10 + V3 %3D Y11 (a) Show that in this case, the overall probability density |Y (0,0)|² = Y* (0,6) Y (8, ø) is independent of both 0 and ø.? (b) Show explicitly that it is properly normalized.
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Transcribed Image Text:4. If an atom is not in a magnetic field or other probe of its angular momentum direction, then
it is equally likely to be found in any allowed state of L2. For the p state, this means that it
can be represented by a superposition of states
Y (0.6) = -1+Yia
(0, ø)
V3
Y1,0 +
V3
(a) Show that in this case, the overall probability density
|Y (0, 4)|² = Y* (0, ¢) Y (0, ø)
is independent of both 0 and ø.2
(b) Show explicitly that it is properly normalized.
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