  which connect the notions of energy \(E\) and momentum \(p\) from the particle picture with those of frequency \(\nu\) and wavelength \(\lambda\) from the wave picture. He noticed that a wave packet of limited extension in space and time can only be built up by the superposition of a number of elementary waves with a large range of wave numbers and frequencies. Denoting the spatial and temporal extensions of the wave packet by \(\Delta x\) and \(\Delta t\), and the extensions in the wave number \(\sigma := 1/\lambda\) and frequency by \(\Delta \sigma\) and \(\Delta \nu\), it follows from Fourier analysis that in the most favorable case \(\Delta x \Delta \sigma \approx \Delta t \Delta \nu \approx 1\), and, using (13), one obtains the relations 