- #1

happyparticle

- 373

- 19

- Homework Statement:
- Why a particle with spin=0 can't posses a dipole moment?

- Relevant Equations:
- ##\langle j'|| \vec{J}|| j \rangle = \hbar \sqrt{j(j+1)} \delta_{jj'}##

Hi,

I would like to know why a particle with spin=0 can't posses a magnetic dipole moment?

Using Wigner-Eckart theorem for ##\langle j,1,m,0|j,m \rangle## I get ##\langle j'|| \vec{J}|| j \rangle = \hbar \sqrt{j(j+1)} \delta_{jj'}##

It seems like the right hand side is the magnetic dipole moment. Thus, j must be 0 for a particle with spin =0.

However, I'm not so sure to understand what j means.

I'll try to explain what I understand.

##\vec{J}## is the total angular momentum and ##\vec{J} = \vec{L} + \vec{S}##, where ##\vec{S}## is the spin.

Furthermore, we have 2 systems (2 particles) ##\langle j'|| \vec{J}|| j \rangle = \hbar \sqrt{j(j+1)} \delta_{jj'}##

where ##j_1 = j, j_2 = 1 , m_1 = m, m_2 =0## and ##j = j_1 + j_2, m = m_1 + m_2##

Are ##j_1, j_2## the total angular momentums for each particle and what exactly are ## m_1, m_2##? Are they quantum number ##m_s## ?

If the spin of the particle is null then ##\vec{S} = 0## which mean ##\vec{J} = \vec{L}##

This is all I know. I can't show that j=0.

I hope this is clear...

thank you

I would like to know why a particle with spin=0 can't posses a magnetic dipole moment?

Using Wigner-Eckart theorem for ##\langle j,1,m,0|j,m \rangle## I get ##\langle j'|| \vec{J}|| j \rangle = \hbar \sqrt{j(j+1)} \delta_{jj'}##

It seems like the right hand side is the magnetic dipole moment. Thus, j must be 0 for a particle with spin =0.

However, I'm not so sure to understand what j means.

I'll try to explain what I understand.

##\vec{J}## is the total angular momentum and ##\vec{J} = \vec{L} + \vec{S}##, where ##\vec{S}## is the spin.

Furthermore, we have 2 systems (2 particles) ##\langle j'|| \vec{J}|| j \rangle = \hbar \sqrt{j(j+1)} \delta_{jj'}##

where ##j_1 = j, j_2 = 1 , m_1 = m, m_2 =0## and ##j = j_1 + j_2, m = m_1 + m_2##

Are ##j_1, j_2## the total angular momentums for each particle and what exactly are ## m_1, m_2##? Are they quantum number ##m_s## ?

If the spin of the particle is null then ##\vec{S} = 0## which mean ##\vec{J} = \vec{L}##

This is all I know. I can't show that j=0.

I hope this is clear...

thank you