What Are the NMR Operators I_x, I_y, and I_z?

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Discussion Overview

The discussion revolves around the nature and definition of the NMR operators I_x, I_y, and I_z, particularly in the context of coherent in-phase heteronuclear spin transfers. Participants explore their roles as spin operators and their relationship to other operators like S_x, S_y, and S_z in quantum mechanics and NMR.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on the operators I_x, I_y, and I_z, noting their frequent mention in literature without clear definitions.
  • Another participant suggests that these operators represent the spin operators for each particle, particularly in the context of coherent in-phase heteronuclear spin transfers.
  • A different participant introduces the Pauli spin matrices, asserting that I_x corresponds to sigma_x and provides a basis set for a 1/2 spin system.
  • One participant questions the interpretation of I_x, I_y, and I_z as identity operators, suggesting that this may not align with their role as spin operators.
  • Another participant emphasizes that spin operators are representations of actions of the special unitary group acting on the same Hilbert space, challenging the notion of different spaces for x, y, z of spin.
  • A participant clarifies that I_x, I_y, I_z are used for spin operators in NMR, while S_x, S_y, S_z pertain to a second spin in a two-spin system.
  • One participant seeks a concrete example of representations of I and S in the context of coherence-order selective in-phase transfer, questioning the implications of their equivalence.
  • A later reply indicates that the participant found a resource clarifying that S and I are operators considered on the combined spin system, resolving some ambiguity.

Areas of Agreement / Disagreement

Participants express differing views on the nature of I_x, I_y, and I_z, with some asserting they are spin operators while others question their classification as identity operators. The discussion remains unresolved regarding the specific roles and definitions of these operators in NMR.

Contextual Notes

There are limitations in the discussion regarding the definitions and assumptions about the operators, as well as the mathematical representations involved in the coherence-order selective in-phase transfer.

Kreizhn
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I'm reading a paper on NMR, and the authors keep referring to the operators [itex]I_x, I_y, I_z[/itex]. What are these operators? I keep finding them mentioned in other papers, but no description of what they are.
 
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In particular, these operators pertain to the discussion of coherent in-phase heteronuclear spin transfers. In this papers the operators mentioned are [itex]S_x, S_y, S_z, I_x, I_y, I_z[/itex]. Am I correct in that these simply represent the spin operators for each particle?
 
The Pauli spin matrices
sigma_x = I_x = 1/2[0 1; 1 0], and so forth.

Which form the basis set for a 1/2 spin system with the |alpha> eigenket being [1;0] and |beta> being [0;1]

And to answer the second question: Yes.
 
I don't know specifically about NMR, but in quantum mechanics that I've come across, when S is spin, I are just the identity operators... but that would probably be obvious from the context.
 
See, but the [itex]S_x, S_y, S_z[/itex] should also represent the spin operators. And in what sense would [itex]I_x, I_y, I_z[/itex] be three separate identity operators?
 
What do you mean we have a different space for x,y,z of spin? A spin operator is a representation of actions of the special unitary group with appropriate dimension for the spin of the particle, acting on the same Hilbert space.
 
Ix,Iy,Iz is the notation used for spin operators in NMR, and Sx, Sy, Sz are the operators on the second spin when you're studying a two-spin system ("I-S").

Trust me. It's been a while since I studied NMR, but I do remember this much. Check out any book on the topic. Or google for some lecture notes or smth.

Edit: http://www.nmrfam.wisc.edu/~milo/notes/paradigm_II.pdf"
 
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So then you're confirming my second post?
 
Kreizhn said:
So then you're confirming my second post?

Yup.
 
  • #10
Okay, the next thing is that given two heteronuclear spin 1/2 particles, the paper is considering the coherence-order selective in-phase transfer from [itex]I^- \to S^-[/itex] where [itex]I^- = I_x - iI_y, S^- = S_x - iS_y[/itex]. But if spin I and spin S have the same representation, what does this transfer amount to? That is, could a concrete example be given for representations of I,S such that this is a nontrivial control problem?
 
  • #11
Nevermind, I think I found a book that's telling me that S and I are operators as considered on the combined spin system. This clears up my ambiguity.
 

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