Why a particle with spin=0 can't posses a magnetic dipole moment?

• happyparticle
In summary, a spin-0 particle cannot have a magnetic dipole moment because it cannot have an intrinsic magnetic moment.
happyparticle
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

happyparticle said:
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
Who told you that a spin 0 particle could not have a magnetic moment? It cannot have a spin magnetic moment (intrinsic magnetic moment) but, as you showed above, it can have an orbital magnetic moment.

-Dan

happyparticle, PeroK, vanhees71 and 1 other person
Why exactly it cannot have a spin magnetic moment?

Can I show it from ##
\langle j'|| \vec{J}|| j \rangle = \hbar \sqrt{j(j+1)} \delta_{jj'}
## ?

happyparticle said:
Why exactly it cannot have a spin magnetic moment?

Can I show it from ##
\langle j'|| \vec{J}|| j \rangle = \hbar \sqrt{j(j+1)} \delta_{jj'}
## ?
Because s = 0...

-Dan

I mean, is it a relationship between s and j ?

happyparticle said:
I mean, is it a relationship between s and j ?
## j = l + s##

happyparticle and topsquark
happyparticle said:
I mean, is it a relationship between s and j ?
The spin magnetic moment of a particle is given by
##\boldsymbol{ \mu } = g \dfrac{e}{2 m} \textbf{S}##

If s = 0 then ##\boldsymbol{ \mu } \mid \psi \rangle = g \dfrac{e}{2 m} \textbf{S} \mid \psi \rangle = \textbf{0} \mid \psi \rangle##

-Dan

happyparticle and DrClaude
Ah I see. I thought that S was the eigenvector and the eigenvalue wasn't necessarily s. thus if s=0 then S wasn't necessarily 0. I think that as usual I had misunderstood.
Thank you

happyparticle said:
Ah I see. I thought that S was the eigenvector and the eigenvalue wasn't necessarily s. thus if s=0 then S wasn't necessarily 0. I think that as usual I had misunderstood.
Thank you
I can't make any sense of this. Are you sure you understand the concepts of operators, eigenvectors and eigenvalues.

malawi_glenn
I thought so, but now you make me doubt.

happyparticle said:
I mean, is it a relationship between s and j ?
You wrote it in the original post

topsquark
malawi_glenn said:
You wrote it in the original post
I was replying to topsquark. I meant if s = 0 why j is automatically 0, that kind of relation.

happyparticle said:
I was replying to topsquark. I meant if s = 0 why j is automatically 0, that kind of relation.
I never said j = 0 because s = 0. j = l + s. If s = 0 then j = l. If l is not zero then the state has an angular magnetic moment, just not a spin angular magnetic moment. Only if j = 0 does the state have no angular magnetic moment.

-Dan

Greg Bernhardt and malawi_glenn
happyparticle said:
I would like to know why a particle with spin=0 can't posses a magnetic dipole moment?
When I first saw this question, I thought it was about a free particle with zero spin. Then @happyparticle brought in the Wigner-Eckart theorem stated talking about orbital angular momentum. Orbital angular momentum presupposes a nucleus which the supposedly zero-spin particle must be orbiting. ##\mathbf{S}## as in ##\mathbf{J}=\mathbf{L}+\mathbf{S}## is the total spin in a many-electron atom and ##\mathbf{S}=0## has nothing to do with a particle with spin = 0 in the original question.

I think the simplest answer to the original question is that spin is an intrinsic property of particles and so is the magnetic moment associated with the spin of the particle. Asking why a particle with zero spin has no magnetic moment is like asking why a bald man has no hair on his head.

Last edited:
hutchphd, gurbir_s, topsquark and 1 other person
Tell me. If S=0, in what direction does the magnetic moment point?

topsquark
Tell me. If S=0, in what direction does the magnetic moment point?
If a man is bald, what color is his hair?

malawi_glenn
kuruman said:
If a man is bald, what color is his hair?
Fish.

-Dan

Something is fishy here. Let's lock the thread for a while until the smell dissipates....

phinds, kuruman and topsquark

1. Why can't a particle with spin=0 possess a magnetic dipole moment?

A particle's spin is a fundamental property that determines its magnetic moment. A particle with spin=0 means that it has no intrinsic angular momentum, hence it cannot possess a magnetic dipole moment.

2. How does spin affect a particle's magnetic properties?

Spin is closely related to a particle's magnetic moment. Particles with non-zero spin have an intrinsic magnetic moment, while particles with spin=0 do not have this property. Therefore, a particle's spin determines its ability to have a magnetic dipole moment.

3. Is spin the only factor that determines a particle's magnetic properties?

No, spin is not the only factor that determines a particle's magnetic properties. The charge of a particle also plays a significant role. A charged particle with spin=0 can still have a magnetic moment due to its charge.

4. Can a particle's spin value change?

No, a particle's spin is an intrinsic property that does not change. It is a fundamental characteristic of a particle and cannot be altered.

5. How does the absence of a magnetic dipole moment affect a particle's behavior in a magnetic field?

A particle with spin=0 and no magnetic dipole moment will not experience any forces or interactions in a magnetic field. This is because it does not have the necessary properties to interact with the magnetic field.

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