Friday, January 16, 2009

Matter waves and wave packet

Moving matter behaves like a wave in quantum mechanics. The wavelength associated with a matter wave can be obtained by dividing the Planck's constant (6.63*10^-34 Js) by its momentum. This wavelength is called the de Broglie wavelength and the matter waves are called the de Broglie waves after the pioneer on matter waves, Louis de Broglie, who was awarded the 1929 Physics Nobel Prize for his discovery of the wave nature of electrons. Since for a massive particle moving with some velocity, the momentum of the particle is large and since this quantity divides the Planck's constant which itself is very small, the de Broglie wavelength is very small and hence we can't visualize the wave nature of the moving matter in day-to-day observation. For example, if a ball of 1kg is rolling on a ground with a speed of 1 m/s, the de Broglie wavelength of the ball is just 6.63*10^-34 m, which is too small to realize as a wave but if we consider atomic and subatomic particles moving at some speed, the wavelength is large enough to visualize the wave nature of matter, at least, doing some precise experiments. For example, the electron microscopes work on the principle that a de Broglie wave is associated with the moving electrons. In atom interferometers, the moving atoms are considered to be waves. In fact, in the modern quantum world, there are a number of devices where matter waves are used.
A wave packet is the unit of a matter wave which carries matter and energy in its direction of propagation at the speed of the wave. It is a small region around a matter particle where there is a very high probability of finding the particle. These wavepackets show properties like that of optical waves ,e.g., diffraction, interference, etc. The following YouTube videos depict how matter waves look like !

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