What does it mean for spins to be anti-phase with each other?

[docnet]

TL;DR Summary

please see below

A pair of spins described by the product operators $I_{1x}I_{2z}$ are said to be anti-phase, while $I_{1y}I_{2y}$ are in phase. What does it mean for a pair of spins to be anti-phase with each other, when their spatial vectors representing direction are orthogonal in space?

Under coupling conditions, a set of spins evolve from anti-phase to in-phase to anti-phase to in-phase. Is "coupling" between two spins a fundamental quantum mechanical property, or can it be reduced to another principle, like entanglement?

Thank you.

 

[vanhees71]

What concrete system/Hamiltonian are you talking about?

 

[docnet]

What concrete system/Hamiltonian are you talking about?

thanks for your reply. here is the description of the system and the hamiltonian for J-coupling. :)

 

[PeterDonis]

here is the description of the system and the hamiltonian for J-coupling

What reference is this from?

 

[vanhees71]

Yes, I'd also need a bit more context. The terminology used in the above source is unfamiliar to me.

 

[docnet]

What reference is this from?

It is from lectures by the Keeler group found here

copy-paste link: http://www-keeler.ch.cam.ac.uk/lectures/

Yes, I'd also need a bit more context. The terminology used in the above source is unfamiliar to me.

The text uses the "product operator formalism" where $I_x=M_x$ refers to the expectation value of the ensemble average (ensemble here means set of identical spins) aka the bulk magnetic momentum. It is unconventional quantum mechanics notation and seems to confuse other students too.

The scalar coupling means two identical spins are interacting by a direct covalent bond. It could be related to the exchange interaction but I am not sure.

 

[docnet]

What concrete system/Hamiltonian are you talking about?

So sorry, the system in question is a pair of directly bonded nuclei in a uniform magnetic field. It is from nuclear magnetic resonance spectroscopy, and it deals with the average expectation values. So the mathematics is based on deterministic, classical reasoning and only deals with rotations in 3D space. $J_{12}$ is the coupling constant, and $t$ is the time under evolution

I am not interested so much in a detailed analysis of the experiments, but interested in a theoretical principle that explains why the spin behaves this strangely under coupling conditions.