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Unformatted text preview: dinates is given by:
= rr + rθθ + r sin θφφ
˙ˆ (6) ˆ
(d) Use the previous part to compute the angular momentum L = × p in terms of r, θ and φ, and then
show that Lz = mr φ sin θ.
Hint! Just think about these three unit vectors - can you very quickly and intuitively argue what the
cross product of r is with each of the spherical unit vectors without doing any calculations at all? Just
be careful of signs.
Extra credit (up to 4 bonus points, but won’t count oﬀ if you don’t do it) If a particle is restricted to move
on the surface of a sphere, r(t) = R, and if angular momentum (in particular Lz ) is conserved (meaning, Lz
doesn’t change with time) and assuming the particle starts its motion somewhere on the z axis, what can
you say about φ at later times?
5. The pair of coupled ODEs
= Ax(t) − Bx(t)y (t)
= −Cy (t) + Dx(t)y (t)
(8) is referred to as the L...
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