(McQuarrie 7.23) Using the definitions of the spherical harmonics Xm verify the linear combinations given below 1/2 5 d₂2 = Yo = 16π (3 cos²0 - 1) 1/2 (Y2 dxz dyz dx²-y² dxy = = = = √2 √2 1 √2 |(x² - 17-²) = ( 15 ) * = (³¹ - Y¹) = 15 = sin cos cos 4πT 15 1/2 = sin cos sin o 4π 15 1/2 = sin² cos 20 16π 1/2 sin² sin 26

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(McQuarrie 7.23) Using the definitions of the spherical harmonics Xm verify the linear
combinations given below
1/2
5
d₂2 = Yo
=
16π
(3 cos²0 - 1)
1/2
(Y2
dxz
dyz
dx²-y²
dxy
=
=
=
=
√2
√2
1
√2
|(x² - 17-²) = ( 15 ) *
= (³¹ - Y¹) =
15
=
sin cos cos
4πT
15
1/2
=
sin cos sin o
4π
15
1/2
=
sin² cos 20
16π
1/2
sin² sin 26
Transcribed Image Text:(McQuarrie 7.23) Using the definitions of the spherical harmonics Xm verify the linear combinations given below 1/2 5 d₂2 = Yo = 16π (3 cos²0 - 1) 1/2 (Y2 dxz dyz dx²-y² dxy = = = = √2 √2 1 √2 |(x² - 17-²) = ( 15 ) * = (³¹ - Y¹) = 15 = sin cos cos 4πT 15 1/2 = sin cos sin o 4π 15 1/2 = sin² cos 20 16π 1/2 sin² sin 26
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