NMR operators

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Main Question or Discussion Point

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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  • #2
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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?
 
  • #3
alxm
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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.
 
  • #4
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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.
 
  • #5
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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 seperate identity operators?
 
  • #6
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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.
 
  • #7
alxm
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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" [Broken]
 
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So then you're confirming my second post?
 
  • #9
alxm
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So then you're confirming my second post?
Yup.
 
  • #10
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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
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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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