Quantum measurements, component amplitude

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

The spectral density is a measure of the amplitude of the M-quantum component of the nuclear spin interaction oscillating at frequency Mlj0 as a result of molecular motion. 

The spectral density is a measure of the amplitude of the M-quantum component of the nuclear spin interaction oscillating at frequency Mo as a result of molecular motion. Of course, we should also recognize that since H(t) varies randomly in time, otherwise identical spin systems will have different H(t) at any given time t. Thus, we need to perform an average over the ensembles of spin systems making up the total sample. We denote this ensemble average by a bar, and thus we replace CM in Eq. (11) with... 

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