Spin-system response from quantum mechanics

2 Spin-system response from quantum mechanics 

The expansion coefficients are complex numbers consisting of amplitude and phase. The Schrodinger equation 

The eigenfunctions are often chosen to depend on time, while the operators are chosen time independent. This choice is referred to as the Schrodinger representation. The change of time of a quantity is called evolution. The evolution of the wave function towards equilibrium is determined by the Schrodinger equation. 

If the Hamilton operator depends on time in a harmonic fashion, the time dependence can be eliminated by transformation into a rotating reference frame in analogy to the transformation of the Bloch equations. A representation in the rotating frame is also called interaction representation in quantum mechanics. If the time dependence is more general, the Schrodinger equation is solved for small enough time increments, during which H is approximately constant. For each of the n time increments At a solution of the form (2.2.46) applies. The complete evolution operator is the time ordered product of the incremental evolution operators. This operator is written in short hand as 

Because the time order of the incremental evolution operators is destroyed by the integral in the exponent, the so-called Dyson time ordering operator is introduced to reestablish the lost time order. 

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