2.9: Particles
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Classical Particles
In this book, we are going to concentrate, almost exclusively, on the behavior of non-relativistic particles of non-zero mass (e.g., electrons). In the absence of external forces, such particles, of mass m, energy E, and momentum p, move classically in a straight-line with velocity
Quantum Particles
Just as light-waves sometimes exhibit particle-like properties, it turns out that massive particles sometimes exhibit wave-like properties. For instance, it is possible to obtain a double-slit interference pattern from a stream of mono-energetic electrons passing through two closely-spaced narrow slits . The effective wavelength of the electrons can be determined by measuring the width of the light and dark bands in the interference pattern. [See Equation (2.7.6).] It is found that
Given the smallness of the de Broglie wavelengths of common particles, it is actually quite difficult to perform particle interference experiments. In general, in order to perform an effective interference experiment, the spacing of the slits must not be too much greater than the wavelength of the wave. Hence, particle interference experiments require either very low-energy particles (because λ∝E−1/2), or very closely-spaced slits. Usually the “slits” consist of crystals, which act a bit like diffraction gratings with a characteristic spacing of order the inter-atomic spacing (which is generally about 10−9 m).
Equation (2.9.3) can be rearranged to give
Because the relation ([e2.19b]) between momentum and wavenumber applies to both photons and massive particles, it seems plausible that the closely-related relation (2.6.1) between energy and wave angular frequency should also apply to both photons and particles. If this is the case, and we can write E=ℏω
Contributors and Attributions
Richard Fitzpatrick (Professor of Physics, The University of Texas at Austin)