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Introduction to the Physics of Waves by Tim Freegarde

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17

Uncertainty and quantum mechanics

17.1 The bandwidth theorem

We have already noted that a wave with a single sinusoidal or complex exponential component extends over all space and time, and that, if we wish to limit its extent, further sinusoidal components spanning a range of frequencies must, as in Section 13.3, be superposed. As with the Gaussian wavepacket of Sections 14.4.1 and 16.5, the tighter the wavepacket is to be confined, the greater the range of frequencies needed. This reciprocal dependence of the frequency range upon the spatial or temporal extent is known as the bandwidth theorem, and is a crucial concept for the analysis of wavepackets.

Pain [66] pp. 376–377Main [60] pp. 206–211Feynman [23] Vol. I, Chapter 38; and Vol. ...

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