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## Homework Statement

Consider the states for which l=4 and s=1/2.For the state wit hteh largest j, and the largest mj, calculate

a) the nagle between L and S

the angle between [itex] \mu_{l}[/itex] and [itex] \mu_{s}[/itex]

c) the angle between J and the +z axis

## Homework Equations

j=l+/-s

## The Attempt at a Solution

the largest possible j is 4 +1/2 which is 9/2.

the largest mj is also 9/2

since mj ranges from -j to +j.

now my prof said that this could be done gemetrically that is

since l=4, then the value of value of L is [itex] \sqrt{4(4+1)}\hbar=3\hbar[/itex]

the projection on the z axis, that is ml may be -4,-3,...,3,4

the spin s=1/2, ms=1/2

the magnitude of the spin angular momentum vector is [itex] \sqrt{3}/2 \hbar[/itex]

usig the projection of both we can draw the vectors and we can find the nagles between them

i was jjust wondering if there was a way of doing this using [itex] \vec{L} \cdot \vec{S} [/tex]

[tex] L \cdot S = |L| |S| \cos \theta [/tex]

the magnitude of L is calcualted above

siilarly for S

but how would one go about calculating L dot S??

thanks for the help!

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