seminoleryan90031 seminoleryan90031

26-01-2024
Physics

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Operator of the angular momentum of two particles of masses m₁,₂ has the form
L=1₁+l₂=−i[r₁× ∇₁]−i[r₂×∇₂]
where r₁,₂ are position vectors of the particles while V₁,₂ refers to vector differentiation with respect to coordinates of particles 1 or 2 . Introducing the relative position vector
r=r₂−r₁
and the center of mass vector
R=m₁r₁+m₂r₂ / m₁m₂
show that the total angular momentum (1) can be presented as a sum of the angular momentum of the relative motion, and the angular momentum of the translational motion of the entire system as a whole. Your answer should be given in terms of r,R and corresponding differential operators Vr and VR.

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