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

The deuteron consists of a proton and a neutron in a state of spin 1 and total angular momentum J = 1. What are the possible angular momentum states for this system.

Another question: Consider a wave function with azimuthal dependence

[tex] \psi(r,\theta,\phi) \propto \cos^2 \phi [/tex]

What are the possible outcomes of a measurement of the z component of the

orbital angular momentum and what are the probabilities of these outcomes?

2. Relevant equations

J = L + S

3. The attempt at a solution

since J =1 and S = 1, and thus -1 and 0. (this becuase suppose a particle had spin 3/2 then [itex] j=l\pm \frac{1}{2}[/itex] and [itex] j = l \pm \frac{3}{2} [/itex]

so then the possible values for l are 2,0,1??

seemingly trivial but i dont quite udnerstand this completely yet soo...

For the second question - it appears that [itex] m_{l}=1 [/itex]

and thus we can calcculate the probability of this measurement using

[tex] c_{n}=\frac{1}{\sqrt{2\pi}} \int_{0}^{2\pi} e^{-i\phi} \cos^2\phi d\phi[/tex]

For ml=1, then

[itex] \left<L_{z}\right>=\hbar [/itex]

Is that right??

Thanks for the help!! it is greatly appreciated!!

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# Homework Help: Question about angular momentum

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