STATISTICAL MECHANICAL THEORY OF MAGNETIC RESONANCE
Abstract
The quantum statistical theory of magnetic resonance considered is that of independent spins in the presence of external static and oscillating fields and a heat bath. An equation of motion is found for only that part of the density operator necessary to calculate properties of the spin system resulting in a linear inhomogeneous integrodifferential equation. The kernel of the integral term, expressed as a power series in the spin-bath interaction, is cut off to a certain order by a Born-like approximation. The memory approximation is also made. Averaging the resulting equation over the bath gives a differential equation for the spin density operator. Conditions for the validity of the series cutooff and the memory approximation have been found. The first is tested by comparing one order in the series with the next higher-order term and the second approximation is tested by solving the integrodifferential equation by the transform method. Bloch's equation is found to agree with the present equation cut off to second order and memory approximated, except for inhomogeneous terms which arise in the present theory from initial conditions. For the case in which the density operator is linearized in the external oscillating field, terms are obtained which represent interference between the external oscillating field and the spin-bath interaction and which were neglected by Wangsness and Bloch. The linearized steady-state solution containing these additional terms has been found for spin 1/2. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1962
- Accession Number
- AD0274740
Entities
People
- P.l. Kelley
Organizations
- Massachusetts Institute of Technology