Basic Principles of Quantum Exchange Coupling

the basic principles of the QEC effect observed in NMR spectroscopy are outlined. Sufficient conditions are specified under which the spin-space Hamiltonian of a set of N-like nuclei in a molecule can be converted into an effective NMR Hamiltonian. The reasoning that follows is a reproduction of long-known ideas, which, however, are sometimes misinterpreted. It is essentially an adaptation of the pertinent formalism 

According to the symmetrization postulate of quantum mechanics, the spin-space state function of a system of N nondifferentiable nuclei must be invariant under any of the A /2 even permutations IV W performed simultaneously on the space (7 ) and spin (S) particles coordinates. Under odd permutations, the state function of N fermions changes sign while that of N bosons remains invariant. 

In order to avoid a possible confusion with the approaches invoking space-fixed spin bases, for the purposes of the present derivation formal definition of the familiar z-component spin functions must be reminded. Thus, for nucleus n of spin I, the symbols where M = —I, and o- 6 -/,-/+ 1./ is the spin 

where (2/ -T 1) = N is the total number of functions X, or the dimension of the spin-space concerned. 

the set of N spin-space states spanning the interesting vibrational manifold will include the Slater determinants (or, for bosons, permanents) l I ) defined according to 

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