Hi Guys, this is from my grad quantum class. I'm pretty stuck and need some help:(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Given four spin-1/2 particles, derive an expression for the total spin state |S,m⟩ ≡ |1,0⟩ in terms of the the four bases |+⟩i , |−⟩i ; i = 1,2,3,4

2. Relevant equations

Clebsch Gordon Coefficients

Raising and lowering operators, etc.

3. The attempt at a solution

OK. So I know the solution has to be of this form:

[tex]|1,0> = a|+++->+b|++-+>+c|+-++>+d|-+++>[/tex]

Now, here is my plan of attack:

First, the state [tex]|2,2>=|++++>[/tex]

I applied the lowering operator to this state repeatedly to find the [itex]|2,0>[/itex] state.

Then I use the condition that:

[tex]<1,0|2,0>=0[/tex] to get: a+b+c+d=0

Also, there is the normalization condition:

[tex]a^2+b^2+c^2+d^2=1[/tex]

So, I have two equations in 4 unknowns. This is my problem.

I can find a third equation by considering <0,0|1,0>=0 however, i don't know the form of the singlet configuration for 4 spins. Any hints on how I can find that?

Still that leaves me still with 3 equations in 4 unknowns. Where do I get the last equation?

Any hints at all would be appreciated. Thanks alot.

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# Homework Help: Addition of 4 spins

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