Lecture15 - Quantum angular-momentum operators Vector...

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1 Physical Chemistry Lecture 15 Angular momentum and the rigid rotor Angular momentum Vector property that describes circular motion of a particle or a system of particles Rigid rotor model: A particle of mass m fixed to a massless rod Examples Swinging a bucket of water Movement of the Earth around the Sun p r L Classical constant-angular- momentum problem Solve for trajectories for constant angular momentum Frequency, , must be constant r must be constant Constant L is provided by the fact that r and are constant t t mr t t t r t ω mr cos sin ) ( sin cos ) ( constant 2 j i p j i r k L Quantum angular-momentum operators Vector definitions Expression by correspondence Form of operators with a fixed r 2 2 2 2 z y x z y x L L L L L L L L L k j i L 2 2 2 2 z y x z y x L L L L x y y x i L z x x z i L y z z y i L
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