Open AccessDENSITY OPERATOR FORMALISM FOR SPIN SYSTEMS WITH PERMUTATION SYMMETRY IN MULTIPLE PULSE AND 2D NMR EXPERIMENTS (Ⅱ)——MULTIPLE QUANTUM PRODUCT OPERATOR FORMALISM
Author(s) -
刘爱琢,
裴奉奎
Publication year - 1990
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.39.154-2
Subject(s) - hamiltonian (control theory) , quantum mechanics , physics , operator (biology) , displacement operator , mathematical physics , mathematics , pure mathematics , quasinormal operator , finite rank operator , mathematical optimization , biochemistry , chemistry , repressor , transcription factor , banach space , gene
Based on the Symmetry-Adapted Product Operator (SPO), the Moltiple Quantum Coherence Product Operator (MQCPO) formalism is introduced in this paper. The modified density operator theory is universal for the description of modern multiple pulse and two-dimensional NMR experiments performed on InS(I = 1/2, 5 = 1/2; n = an arbitray integer number) spin systems. In fact, MQCPO is a Hermitian combination of irredusible tensor operators for a compsite particle, and reveals symmetry properties of the spin system in a different aspect from SAPO. There exist simple linear relations between MQCPO and SAPO for In(I = 1/2, n = 2,3) spin systems, the SAPO forms of MQCPO are listed as a usual example. MQCPO shows a simple cyclic commutation relationship with the free procession Hamiltonian, but not with the Hamiltonian of a pulse effect. Therefore, MQCPO is convenient for description of evolution period. Using the linear relations between MQCPO and SAPO, as well as the permutation properties for the coordinate indices of Cartesian components in a SAPO, the description of a pulse action tarns out to be easy and direct under the "z"-representation. Analyses of the pulse sequences for heteronuclear spectra editing and spin topology filtration have shown the power of this formalism.