A.Cemal Eringen's Continuum Physics PDF

By A.Cemal Eringen

ISBN-10: 0122408047

ISBN-13: 9780122408045

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Sample text

We consider only the position-momentum uncertainty relations for now, given their importance. 85), generalizing the reasoning presented there to three-dimensional space; these imply that the more exactly one determines the position in a particular direction, the less well-defined will be the momentum in this direction, and vice versa. Notice that the above relations refer to simultaneous knowledge of the position and momentum in a predetermined direction, but they do not at all restrict the precision with which position or momentum can be measured.

In particular, for such pure, identically prepared systems, the measurement of any observable always gives the same results. Nevertheless, for classical many-particle systems, limitations of a practical nature restrict such total control of the state. Only a few attributes of the system are generally fixed, and knowledge of its state suffices only to specify some extended region in phase space. We then speak of a mixed state (one for which we have incomplete information), and measurements of an observable on identically prepared systems will, in general, present some dispersion.

This beam, which we assume to be directed along the Ox axis, enters a highly evacuated chamber in which an inhomogenous magnetic field B has been established Because of the shape of the pole pieces which produce it, the field is basically directed along the 0 z axis in the region traversed by the beam and also has a large gradient in the same direction. 1.. ). Because of the precessional motion, {Lx and {Ly oscillate rapidly, while {Lz remains constant, so that, due to the oscillations, a force of magnitude {L z 8 B j 8 z acts on the center of mass in the 0 z direction on average.

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Continuum Physics by A.Cemal Eringen

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