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

  • Context: Undergrad 
  • Thread starter Thread starter docnet
  • Start date Start date
  • Tags Tags
    Mean
Click For Summary

Discussion Overview

The discussion centers around the concept of spins being anti-phase with each other, particularly in the context of quantum mechanics and nuclear magnetic resonance (NMR) spectroscopy. Participants explore the implications of spin coupling, the terminology used, and the underlying principles governing these phenomena.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant describes anti-phase spins using product operators ##I_{1x}I_{2z}## and contrasts them with in-phase spins represented by ##I_{1y}I_{2y}##, questioning the meaning of anti-phase in the context of orthogonal spatial vectors.
  • There is a query about whether the coupling between spins is a fundamental quantum mechanical property or if it can be reduced to another principle, such as entanglement.
  • Several participants request clarification on the specific system or Hamiltonian being discussed, indicating a need for more context.
  • A participant mentions that the terminology used in the reference material is unfamiliar, suggesting a potential barrier to understanding the concepts being discussed.
  • Another participant provides a description of the system involving a pair of directly bonded nuclei in a uniform magnetic field, relating it to NMR spectroscopy and the average expectation values.
  • There is mention of the "product operator formalism" and its unconventional notation, which seems to confuse some participants.
  • One participant expresses interest in the theoretical principles explaining the behavior of spins under coupling conditions rather than a detailed experimental analysis.

Areas of Agreement / Disagreement

Participants generally seek clarification and context regarding the terminology and concepts, indicating that there is no consensus on the understanding of anti-phase spins or the implications of spin coupling. Multiple competing views and uncertainties remain regarding the fundamental nature of coupling and its relation to other principles.

Contextual Notes

Limitations include the reliance on specific terminology that may not be universally understood, as well as the potential for confusion arising from unconventional notation in the product operator formalism. The discussion also hinges on assumptions about the nature of spin coupling and its theoretical underpinnings.

docnet
Messages
796
Reaction score
486
TL;DR
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.
 
Physics news on Phys.org
What concrete system/Hamiltonian are you talking about?
 
  • Like
Likes   Reactions: bhobba
vanhees71 said:
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. :)
Screen Shot 2021-03-21 at 10.59.19 AM.png
Screen Shot 2021-03-21 at 10.59.39 AM.png
Screen Shot 2021-03-21 at 11.00.09 AM.png
 
  • Like
Likes   Reactions: vanhees71
docnet said:
here is the description of the system and the hamiltonian for J-coupling

What reference is this from?
 
  • Like
Likes   Reactions: docnet and vanhees71
Yes, I'd also need a bit more context. The terminology used in the above source is unfamiliar to me.
 
  • Like
Likes   Reactions: docnet
PeterDonis said:
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/

vanhees71 said:
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.
 
vanhees71 said:
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.
 

Similar threads

  • · Replies 71 ·
3
Replies
71
Views
6K
  • · Replies 49 ·
2
Replies
49
Views
5K
  • · Replies 74 ·
3
Replies
74
Views
5K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 87 ·
3
Replies
87
Views
8K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 8 ·
Replies
8
Views
7K