(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1) For l=3, find the possible angles that the orbital angular momentum vector(L) makes with the z axis? Here the magnetic field acts along the z axis. l is the orbital quantum number.

2. Relevant equations

3. The attempt at a solution

I solved it in the following way:

Let m(l) represent the magnetic quantum number. Phi is the angle between L and z axis. For l=3, m(l)=-3,-2,-1,0,1,2,3

m(l)x(h/2(pi)) = L[cos(phi)]{[lx(l+1)]^(1/2)}(h/2(pi))

i.e. cos(phi) = m(l)/{[lx(l+1)]^(1/2)}

For m(l) = 3,

Cos(phi) = 3/(12^(1/2))

phi = 30 degrees

For m(l) = 2,

Cos(phi) = 2/(12^(1/2))

phi = 54.7 degrees

For m(l) = 1,

Cos(phi) = 1/(12^(1/2))

phi = 73.2 degrees

But the answer given in my book is 60, 35.3 and 16.8 degrees. I would get this answer if I take sine instead of cosine.

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# Angles made by angular momentum vector with magnetic field

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