RgdRot3D

RgdRot3D - Rigid Rotor - Rotation in Three Dimensions 2 2 h...

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Ψ= Y l, m l = Θ(θ29 Φ(φ29 l m l Y l, m l 0 0 (1/4 π ) 1/2 1 0 (3/4 π ) 1/2 cos θ ± 1 ± (3/8 π ) 1/2 sin θ e ± i φ 2 0 (5/16 π ) 1/2 (3 cos 2 θ -1) ± 1 ± (15/8 π ) 1/2 cos θ sin θ e ± i φ ± 2 ± (15/32 π ) 1/2 sin 2 θ e ± i2 φ Rigid Rotor - Rotation in Three Dimensions h 2 2m 2 Ψ + V Ψ=ΕΨ V = 0 2 = 2 x 2 + 2 y 2 + 2 z 2 x y z θ φ r m 2 = 1 r 2 r 2 r + 1 r 2 Λ 2 (angular momentum operator) 2 = – h 2 Λ 2 Λ 2 = 1 sin 2 θ 2 ∂φ 2 + 1 sin θ ∂ θ sin θ ∂θ h 2 2mr 2 Λ 2 Ψ =ΕΨ h
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This document was uploaded on 02/22/2012.

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