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SOLVED: Resonance, the evolution operator U(t) in the rotating frame given by5.5.6 The rotating-wave approximation in NMR Instead of the rotating field of (5.22), We shall use field B(t) parallel to:iw I(0,cos δ, sin δ) expU(t) = expB(t) = 2B cos(ωt φ)rotation operator of angleabout an axis of componentsWe define the state vector |F(t)) in the rotating frame with angular velocityIWu[ Ie(θ) I(θ)sin θ n=0Iz(θ)Ie(θ) = 0Thus the angle θ allows one to choose the rotation axis. One may (ri
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The progressive wave equation is a fundamental concept in physics that describes the behavior of waves as they propagate through a medium. It is often expressed in the form:[y(x, t) = A sin(kx - omega t phi)]Here's a breakdown of the components:- (y(x, t)): Represents the displacement of the wave at a given position (x) and time (t).- (A): Amplitude, determining the maximum displacement from the equilibrium position.- (k): Wave number, indicating how many wavelengths exist in a unit distance.- (
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