Formation, 2 Hamiltonian operator

Finally some other developments are briefly mentioned for the sake of completeness. These include the work of Sposito and Babcock 184> which bears close resemblance to the partitioned potential methods. Their idea is to solve the quantum mechanical energy spectrum of the complex using only the empirical potential function as the potential operator in the Hamiltonian. This spectrum then leads to calculations of temperature-dependent energies of formation. 

Consider the free procession signal acquired as a function of time t after the spin-echo formation at time t. We shall presume that the sole term acting in the Hamiltonian after the echo center is due to the Larmor precession at frequency in the uniform field, where the use of the subscript i allows for the range of chemical shifts in the NMR spectrum. This precession contributes an evolution operator exp(iWo,t ->, ) to the density matrix so that we can rewrite Eq. (39) as... 

The most general approach to the formation of the effective operator of the intersite virtual phonon exchange interaction is based on the canonical shift transformation of the Hamiltonian... 

The superscript H on the square bracket in (8.3.4) indicates that the Liouville expression inside the bracket needs to be transformed back into Hilbert space before multiplication with the Hilbert-space operator 1 = 1 - ily = I- and formation of the trace. Inverse Fourier transformation over k produces an image of the spin density. Given the form of the density matrix after the initial pulse, the spin density corresponds to 1+ (r). It is weighted by the phase evolution under the internal Hamiltonians Hx(r) during the space-encoding time ti,... 

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