Second Quantization Method in Two-Dimensional NMR Spectroscopy

  • W. Nosel
  • P. S. Allen
Conference paper


The second quantization formalism is applied to calculation of two-dimensional NMR spectra for a spin-1/2 systems.

The time evolution of a density operator σ(t) under rf pulses and under scalar interaction is expressed in linear operator form
$$ \sigma (t) = \Sigma {A_{ij}}(t)a_i^ + {a_{j,}} $$
where the coefficients Aij(t) are determined by the equation
$$ i{A_{ij}} = {\Sigma _k}({H_{ik}}{A_{kj}} - {A_{ik}}{H_{kj}}). $$

As an example, the results of calculations of two- dimensional correlation spectra for a strongly coupled two-spin system are presented.

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • W. Nosel
    • 1
  • P. S. Allen
    • 2
  1. 1.Institute of PhysicsJagellonian UniversityCracowPoland
  2. 2.NMR Facility, Department of Applied Sciences in MedicineUniversity of AlbertaEdmontonCanada

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