Transfer matrix element, definition

The amplitude of electron tunneling transfer with simultaneous change of the vibrations in the case of the non-adiabatic asymptotics (56) may be found, if to substitute the expression (56) instead of F ) to the definition (9) and the acceptor wave function in the matrix element (9) should be its total expression... 

This is the usual magnetic resonance lineshape for transitions in a two-level system without damping. At resonance the population oscillates sinusoidally between the two states (this is known as Rabi oscillation). A n-pulse is an on-resonance pulse with 2bx = Tt, which transfers all the population from state (0) to state (c). In Section 15.4.3 we will discuss how this can be used in a molecular beam to map out the fields along the beamline. An on-resonance 7r/2-pulse 2bz = n/2) drives the transition only half-way, creating an equal superposition of states (0) and (c) with a definite relative phase. The density matrix element describing this coherence at the end of... 

Here S,- is the transfer matrix operating between lines (or planes) i and / -F 1. In the case of regular shapes, such as squares or cubes, all planes being identical, S2 = S3 = = S 1 = S, with u and v being the vectors extracting the states accessible to the first and last lines (or planes), respectively. Superscript T denotes the transpose. Elements of u are either 0 or the number of ways to transit, depending on the possible occurrence of the state i at the starting line (plane). A similar definition holds for v. 

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