A quantum wave builds up in a resonant cavity between the straight and curved walls, when waves are arriving from below. Most of the wave energy is reflected back, but a surprisingly large fraction of it gets through the tiny hole if the wavelength is just right to make the cavity resonant. Westervelt Resonator-In this image, a quantum wave builds up in a resonant cavity between the straight and curved walls, when waves are arriving from below. Most of the wave energy is reflected back, but a surprisingly large fraction of it gets through the tiny hole if the wavelength is just right to make the cavity resonant. Prof. Robert Westervelt and his research group invented the "Westervelt resonator" around 1995 at Harvard University, for the purpose of investigating electron waves. In this picture you see various aspects of waves all acting together: reflection, diffraction, and resonance. The whole device is just a few microns across, or smaller than a bacterium.
The idea is to place a semicircular reflecting mirror facing a wall punctured by a little hole. Electrons are aimed at the wall, and most hit it and bounce back. But there are exceptions to this. Some electrons make it through the little hole, where they emerge and then get reflected back to the wall by the mirror. Most of these reflect back to the mirror, and so forth. Since not many electrons can get through the hole, you would think it would be dark (or quiet) in the "cavity" between the wall and the mirror (think of light, or sound, which are also waves). But as the speed of the electrons is increased, their wavelength gets shorter, according to the deBroglie formula l = h/(m v), where m is the mass, v is the velocity, and l is the wavelength. Some speeds are just right to fit a round number of wavelengths in the cavity, and a big buildup of waves takes place in there, the "resonance". If this were sound coming through a small hole in a wall, it would still be very loud in "room" at that one wavelength, or frequency of sound. The resonance is rare and usually it is pretty quiet in the cavity. Finally, even though the electrons would be trapped in the cavity (except for going back through the hole), they manage to leak out the sides. This is diffraction; waves do this, but particles cannot.
Ordered Motion and Crystals || Quantum Random Waves || Classical Electron Flow || Quantum Modes and Classical Analogs || Quasi Classical Correspondence, Quantum Scars || Quantum Resonances || Classical Collisions || Quantum Quasi Crystal || Maps || Caustics || Rogue Waves || Screen Savers || Sound
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