Undergrad Particle field strength and sensitivity

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SUMMARY

The discussion centers on the comparative magnetic moments of electrons and protons, highlighting that the magnetic moment of an electron is approximately 700 times greater than that of a proton. In a magnetic field, the energy of an unpaired electron is significantly higher than that of an unpaired proton, with specific values noted for various nuclei. The interaction energies between magnetic particles, particularly the electron-proton interaction being 108 times greater than the proton-proton interaction, are analyzed, emphasizing the differences in coupling energies in nuclear magnetic resonance (NMR).

PREREQUISITES
  • Understanding of magnetic moments in quantum mechanics
  • Familiarity with nuclear magnetic resonance (NMR) principles
  • Knowledge of electron and proton spin characteristics
  • Basic concepts of magnetic field interactions
NEXT STEPS
  • Research the principles of electron-proton interactions in quantum mechanics
  • Study the effects of J-J coupling in nuclear magnetic resonance (NMR)
  • Explore the differences in magnetic moments across various nuclei
  • Investigate the implications of magnetic field strength on particle interactions
USEFUL FOR

Physicists, quantum mechanics researchers, and students studying nuclear magnetic resonance and particle physics will benefit from this discussion.

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The magnetic moment of an electron is about 700 times bigger than that of a proton. Both have spin 1/2, but in equal external magnetic field, the energy of an unpaired electron is about 700 times bigger than the energy of an unpaired proton.
(All nuclei other than the triton have magnetic momenta smaller than the proton. The weakest magnetic moments, like Fe-57, Au-197 and IIRC some Ir are in the region of 1,5% of proton magnetic moment).
But how are magnetic particles affected by magnetic fields of each other?
In protium atom, of one unpaired proton and one unpaired electron, the relative orientations are split by 1420 MHz.
In molecules, the energy of a proton in the magnetic field of a nearby proton - that is, the J-J coupling of NMR - is typically in the order of magnitude of 6...8 Hz. Sometimes slightly more.
That is 108 times less than the energy of the proton in the field of an electron.
Why is the electron-proton interaction energy 108 times bigger than proton-proton interaction energy, rather than just 103 times bigger like the electron-external field interaction energy?
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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