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Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. At all scales where measurements have been practical, matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave.
Matter waves of molecules as large as carbon \(C_{60}\) have been measured. All physical objects, small or large, have an associated matter wave as long as they remain in motion. The universal character of de Broglie matter waves is firmly established.
We have described matter waves in terms of the momentum and energy of the particle, but it is still a wave, and as such possesses wave properties like wavelength and frequency. We can extract these quantities directly from the wave function by comparing it to a wave function of a general harmonic wave. We’ll start with the matter wave’s ...
28. Feb. 2024 · Matter waves, also known as de Broglie waves, are defined scientifically as the wave-like behavior exhibited by particles at the quantum scale. According to de Broglie’s hypothesis, any moving particle or object has an associated wave whose wavelength is inversely proportional to the momentum of the particle.
- De Broglie
- Schrödinger
- Heisenberg
- Electron Microscopes
- History and Miscellany
Combine the two equations for momentum. This was basically Louis de Broglie's doctoral thesis of 1924. Davisson-Germer experiment. Electrons diffracted after being reflected off a single crystal of nickel. A person entering a room with more than one entrance will always enter through one of them, not all of them at the same time. An electron, on th...
Erwin Schrödinger (1887–1961) Austria, Abhandlungen zur Wellenmechanik. Wave equation for matter reminiscent of Maxwell's equations for electromagnetic waves. The story I heard is that Schrödinger went to Switzerland with two goals: to keep his mistress happy and to derive a wave equation for matter. How successful he was with the former is open to...
Quote to get things started. The defining feature of the microscopic world is the wave-particle duality. Whenever we observe elementary entities (like electrons or photons) they appear as a localized events. A single photon can be observed as a tiny dot on a photographic plate. A single electron can be observed as a tiny flash on a television scree...
thomson-reid Electron Microscope 1. Transmission Electron Microscope (TEM): Produces a shadowgraph like an x-ray. The first electron microscope was built in 1931 by Ernst Ruska and Max Knoll at the Berlin Technische Hochschule. 1.1. Scanning Transmission Electron Microscope (STEM) 2. Scanning Electron Microscope (SEM): Basically a scanner that read...
Quantum mechanics is like a student who always gets the correct answer to the first question in an exam, but never the second. A good simple application. Electrons have very little mass and therefore occupy a lot of volume. Protons are much more massive and occupy very little volume. Absolute zero does not imply absolute rest. Zero point energy. vi...
Matter waves of molecules as large as carbon C 60 C 60 have been measured. All physical objects, small or large, have an associated matter wave as long as they remain in motion. The universal character of de Broglie matter waves is firmly established.
Solution: λ = h/p, E = p 2 / (2m), p = √ (2mE), λ = h/√ (2mE). The energy of the electron is 25000 eV * 1.6*10 -19 J/eV = 4*10 -15 J. λ = (6.626*10 -34 Js)/√ (2*9.1*10 -31 kg*4*10 -15 J) = 7.8*10 -12 m. This wavelength is approximately 100 times smaller than the typical size of an atom. Problem:
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