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Spectral geometry is a field in mathematics which concerns relationships between geometric structures of manifolds and spectra of canonically defined differential operators. The case of the Laplace–Beltrami operator on a closed Riemannian manifold has been most intensively studied, although other Laplace operators in differential geometry ...
The later discovery in quantum mechanics that spectral theory could explain features of atomic spectra was therefore fortuitous. Hilbert himself was surprised by the unexpected application of this theory, noting that "I developed my theory of infinitely many variables from purely mathematical interests, and even called it 'spectral analysis ...
It is not known if it can be ℵ 1 if the continuum hypothesis is false: this is called the Vaught conjecture and is the main remaining open problem (in 2005) in the theory of the spectrum. Morley's problem was a conjecture (now a theorem) first proposed by Michael D. Morley that I(T,κ) is nondecreasing in κ for uncountable κ.
Metameric matches are quite common, especially in near neutral (grayed or whitish colors) or dark colors. As colors become brighter or more saturated, the range of possible metameric matches (different combinations of light wavelengths) becomes smaller, especially in colors from surface reflectance spectra.
The fine structure energy corrections can be obtained by using perturbation theory.To perform this calculation one must add three corrective terms to the Hamiltonian: the leading order relativistic correction to the kinetic energy, the correction due to the spin–orbit coupling, and the Darwin term coming from the quantum fluctuating motion or zitterbewegung of the electron.
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Three weaker bands of C 60 + were found in interstellar spectra soon afterwards, resolving one of the earlier objections raised by Jenniskens. [22] New objections were raised by other researchers, [ 23 ] but by 2019 the C 60 + bands and their assignment had been confirmed by multiple groups of astronomers [ 24 ] [ 25 ] and laboratory chemists.
The result of fitting a set of data points with a quadratic function. Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum based on a least-squares fit of sinusoids to data samples, similar to Fourier analysis.