By Orly Alter

ISBN-10: 0471283088

ISBN-13: 9780471283089

A groundbreaking examine the character of quantum mechanics With new applied sciences allowing the commentary and manipulation of unmarried quantum platforms, the quantum conception of dimension is speedy changing into an issue of experimental research in laboratories world wide. This unique new paintings addresses open basic questions in quantum mechanics in mild of those experimental advancements. utilizing a unique analytical technique built via the authors, Quantum dimension of a unmarried approach presents solutions to 3 long-standing questions which have been debated by way of such thinkers as Bohr, Einstein, Heisenberg, and Schrodinger. It establishes the quantum theoretical limits to details received within the size of a unmarried process at the quantum wavefunction of the procedure, the time evolution of the quantum observables linked to the approach, and the classical potentials or forces which form this time evolution. The technological relevance of the speculation can be confirmed via examples from atomic physics, quantum optics, and mesoscopic physics. appropriate for pros, scholars, or readers with a normal curiosity in quantum mechanics, the ebook beneficial properties fresh formulations in addition to funny illustrations of the elemental thoughts of quantum dimension. Researchers in physics and engineering will locate Quantum dimension of a unmarried approach a well timed advisor to 1 of the main stimulating fields of technology this day.

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Example text

8) 20 QUANTUM MEASUREMENT OF A SINGLE SYSTEM Consider now the statistics of both measurement results ijl and ij2. , the width of the probability density P(G1),cannot be estimated using only one of the measurement results ijl or ij2, since (ij1)2cannot be estimated. If ijl and ;i2 were independent results, obtained from two different quantum systems, that belong to the same ensemble and were, therefore, initially in the same quantum state, their correlation would be (4142) = (41>(42> = (W2. 11) This correlation then would provide the missing information about (ij1)2,and (Aij;) could be estimated using both measurement results.

As the photon-number probability density narrows, the average step size of this quantum Brownian motion decreases. The statistical variance of nk, saturates, and equals the initial width of the photon-number probability density (the initial uncertainty associated with the photon-number of the squeezed state) At. At the same time the squeezed state is reduced to a photonnumber eigenstate. The measured state therefore undergoes quantum Brownian motion, which is saturated due to its continuous collapse.

This is because the changes in the wavefunction due to any process of repeated quantum measurements are always governed by the reduction. 5 QND MEASUREMENT AS A PROTECTIVE MEASUREMENT Under what conditions would a Q N D measurement be also a protective measurement, which does not change the quantum state of the measured system at all? Consider again the general quantum measurement process of the observable 4 of a signal system, which is intially in the state and = II,/I)~~($I. The three stages is described by the density operator of this measurement process are described completely by the probability-amplitude operator ?

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