Transformed Hamiltonian

Equations (ll-377)-(ll-381) for the field operators entail that under time inversion the interaction hamiltonian transforms like a scalar... 

It is also of interest to study the "inverse" problem. If something is known about the symmetry properties of the density or the (first order) density matrix, what can be said about the symmetry properties of the corresponding wave functions In a one electron problem the effective Hamiltonian is constructed either from the density [in density functional theories] or from the full first order density matrix [in Hartree-Fock type theories]. If the density or density matrix is invariant under all the operations of a space CToup, the effective one electron Hamiltonian commutes with all those elements. Consequently the eigenfunctions of the Hamiltonian transform under these operations according to the irreducible representations of the space group. We have a scheme which is selfconsistent with respect to symmetty. 

The so-called HORROR experiment by Nielsen and coworkers [26] introduced continuous rf irradiation recoupling to homonuclear spin-pairs and initiated the later very widely used concept of /-encoded recoupling. Using a irreducible spherical approach as described above, the HORROR experiment (Fig. 2d) is readily described as starting out with the dipolar coupling Hamiltonian in (10) and x-phase rf irradiation in the form Hrf = ncor(Ix +SX), also here without initial constraint on n. The dipolar coupling Hamiltonian transforms into tilted frame (rotation n/2 around Iy + Sy)... 

All the terms in the molecular Hamiltonian transform as the totally symmetric irreducible representation (irrep) of the molecular point group. Symbolically,... 

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