WE theorem to evaluate matrix elements

[pollo]

Hi!

In my work I use the WE theorem to evaluate matrix elements. F being the total spin and m the projection onto the z-axis, I am using:

<JIFm|r_(-q)|J'IF'm'>=(-1)^(F'+m'-m)<Fm1q|F'm'>sqrt(2F+1)sixj(F, F', 1:J',J,I)<J'||r||J>

I have a problem with the (-1)^ part which I suspect to be wrong, but have not been able to find a formula to compare a check. Am quite sure the rest is right. Could somebody help and tell what should be in the exponent?

 

[DeShark]

hi!

In my work i use the we theorem to evaluate matrix elements. F being the total spin and m the projection onto the z-axis, i am using:

<jifm|r_(-q)|j'if'm'>=(-1)^{f'+m'-m}<fm1q|f'm'>\sqrt{2f+1}sixj(f, f', 1:j',j,i)<j'||r||j>

i have a problem with the (-1)^ part which i suspect to be wrong, but have not been able to find a formula to compare a check. Am quite sure the rest is right. Could somebody help and tell what should be in the exponent?

I have the theorem as:

$$<\tau J M|T_q^{(k)}|\tau' J' M'> = {1 \over {\sqrt{2J+1}}}<\tau J ||T^{(k)}||\tau' J'><J' k M' q| J M>$$

where $$<\tau J ||T^{(k)}||\tau' J'>$$ is the reduced matrix element.

Unfortunately I couldn't make head nor tail of the function you're trying to use. Maybe I'll've been of some help. Either way, this has been here for a couple of days with no reply, so maybe this will help the discussion.

 

[Entropia]

Hello!

The WE theorem is a useful tool in evaluating matrix elements, particularly in the context of quantum mechanics and angular momentum. The (-1)^ exponent in your equation is related to the parity of the system and can be either +1 or -1 depending on the quantum numbers involved. In order to determine the correct value, you will need to consider the parity of the states involved and use the appropriate selection rules. I would recommend consulting a textbook or a more experienced colleague for assistance in determining the correct value for your specific system. Additionally, double-checking your calculations and using a formula sheet as a reference can also help in verifying the accuracy of your results. Good luck with your research!