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  • https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Direct_Energy_(Mitofsky)/06%3A_Photovoltaics/6.03%3A_Crystallography_Revisited
    Just as we can get from one lattice point to another by traveling integer multiples of the \(\overrightarrow{a_\mathfrak{n}}\) lattice vectors, we can get from any one point to the next of the recipro...Just as we can get from one lattice point to another by traveling integer multiples of the \(\overrightarrow{a_\mathfrak{n}}\) lattice vectors, we can get from any one point to the next of the reciprocal lattice by traveling integer multiples of the \(\overrightarrow{b_\mathfrak{n}}\) lattice vector. If a beam of light shines on a crystal where the wavelength of light is close to the crystal spacing, light will be diffracted, and the diffraction pattern is related to the reciprocal lattice.
  • https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Direct_Energy_(Mitofsky)/13%3A_Thomas-Fermi_Analysis/13.02%3A_Preliminary_Ideas
    The derivation of the Thomas Fermi equation involves derivatives of vectors in spherical coordinates

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