Very difficult problem for you

[stefano]

I need to write an eigenstate of total angular momentum of three particle.

In particular I use the j=5/2 orbital of single-particle (with six projections...) and I have to construct eigenstate for J=j_1+j_2+j_3 to write down anti-symmetric eigenstates.

For example, I tried to construct J=5/2 M=1/2 (it would be composed by two determinants) but I didn't be able to to this; I coupled first j_1+j_2 and then j_12 with j_3 (the 3rd components of j of single particle is fixed to have M=m_1+m_2+m_3,) but I didn't obtaine any determinant.

Who can be able to calculate this for me?

Thank's

 

[stefano]

Or does someone know some utility or program to do this?

 

[R0man]

for reaching out for help with this difficult problem. Constructing eigenstates of total angular momentum for multiple particles can be a complex and challenging task. In order to write down an anti-symmetric eigenstate for J=j_1+j_2+j_3, you will need to use the Clebsch-Gordan coefficients to couple the individual angular momenta of each particle. This process can be quite involved and requires a thorough understanding of angular momentum and its properties.

I recommend seeking the help of a physics tutor or consulting with a professor or graduate student in your university's physics department for assistance with this problem. They will have the expertise and resources to guide you through the calculations and help you construct the desired eigenstate.

In the meantime, you can also try looking for online resources or textbooks that provide step-by-step examples of constructing eigenstates for multiple particles. Practice and patience are key in mastering complex problems like this.

Best of luck with your work and don't hesitate to seek help when needed. Remember, it's always better to ask for assistance than to struggle alone.