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Lecture 5 - EEE 352 LECTURE 05 Properties of Matter...

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EEE 352: LECTURE 05 Properties of Matter Waves (how can we think of particles as waves?) * De Broglie relation (de Broglie decided to apply electromagnetic wave ideas to the electrons) * Matter waves Wave function Both particles and normal waves create interference patterns, when we look at the “quantum scale”, a result which is only usually related to the wave properties of things like photons.
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We are led to conclude that ALL “things”, whether electrons or photons or automobiles or …… are both particle and wave! Which property we “measure” depends upon the type of measurement that is carried out. * The two-slit experiment is a wave-like measurement * The photo-electric effect is a particle-like measurement This wave-particle duality is a part of the principle of complementarity. The complementarity principle is considered as Neils Bohr’s important contribution, yet he had trouble fully accepting a wave-based theory that was due to Schrödinger and the electron wave concept of de Broglie. Heisenberg never really accepted the wave concept for particles. The “NEW” Mechanics: QUANTUM MECHANICS
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These different views of quantum mechanics are today called “interpretations.” The Copenhagen (Bohr, Heisenberg, Pauli) interpretation is accepted by perhaps a majority, but not by all. The probability interpretation of Copenhagen creates problems with causality and with reality—nothing happens unless we measure it. Other more well-known interpretations are the “many-worlds” view of Everett, the “consistent histories” of Griffiths, and Bohm’s particle AND wave interpretation. These are still being argued today by philosophers and scientists. But, the existence of the wave nature is clearly there, in both theory and experiment. We will proceed with this, without worrying about what the “real” theory is, or should be.
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Now, this led to another important (and new) concept. If the particle is a wave, where is it ? If we have a wave packet corresponding to the particle, it has a non-zero extent: Δ x
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But, a wave packet is composed of several, closely spaced frequencies, so that there is also a Δω . Now, so that and
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In fact, Werner Heisenberg postulated that the Uncertainty Principle would require that Werner Heisenberg Nobel Prize in Physics, 1932
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The De Broglie Relation ELECTRON GUN We found that particles showed interference, and therefore behaved as waves. But, the interference period is related to the wavelength of the wave—particles must have a wavelength! The idea of a wavelength corresponding to quantum structures was put forward by Louis de Broglie, in his doctoral thesis at the University of Paris (1923), when he asserted that particles had wave-like properties Prince Louis-Victor de Broglie Nobel Prize in Physics, 1929
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The De Broglie Relation For particles, and particularly for photons, the energy can be given by Einstein’s famous formula: But, the energy of the photon is also given by Planck’s famous law: so that The momentum of the photon is said to be mc=p de Broglie’s
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