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2.S: Foundations of Quantum Mechanics (Summary)

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  • Around 1900 several experimental observations were made that could not be explained, not even qualitatively, by existing physical laws. It therefore was necessary to invent (create) new concepts: quantization of energy and momentum, and a momentum-wavelength relation. In 1900 Planck proposed that electron oscillations in matter were quantized, and their energy was related by E = hν to the frequency of radiation emitted by a hot object. In 1905 Einstein proposed that electromagnetic radiation, light, also was quantized, consisting of photons, each with energy E = hν. In 1914 Bohr used this energy-frequency relationship together with the quantization of angular momentum, \(M = n \hbar\), to construct a model of the hydrogen atom that was consistent with its luminescence spectrum. In 1922 Compton explained the inelastic scattering of x-rays by matter by treating the x‑rays as particles with momentum p = h/λ. In 1924 de Broglie argued that particles should then have the properties of waves with a wavelength λ. This suggestion led Schrödinger to develop the general underlying theory of Quantum Wave Mechanics in 1925. The wave-like properties of electrons and the validity of the de Broglie relationship were demonstrated directly by Thomson’s and Davisson and Germer’s diffraction experiments in 1926 and 1927.

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