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Principal Series
Principal series may refer to: * Principal series (spectroscopy), series of spectral lines * Principal series representation In mathematics, the principal series representations of certain kinds of topological group ''G'' occur in the case where ''G'' is not a compact group. There, by analogy with spectral theory, one expects that the regular representation of ''G'' will ... , topological group theory, {{disambiguation Science disambiguation pages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principal Series (spectroscopy)
In atomic emission spectroscopy, the principal series is a series of spectral lines caused when electrons move between p orbitals of an atom and the lowest available s orbital. These lines are usually found in the visible and ultraviolet portions of the electromagnetic spectrum. The principal series has given the letter ''p'' to the p atomic orbital In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in an ... and subshell. The lines are absorption lines when the electron gains energy from an s subshell to a p subshell. When electrons descend in energy they produce an emission spectrum. The term principal came about because this series of lines is observed both in absorption and emission for alkali metal vapours. Other series of lines appear in the emission spectrum only and not in the absor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principal Series Representation
In mathematics, the principal series representations of certain kinds of topological group ''G'' occur in the case where ''G'' is not a compact group. There, by analogy with spectral theory, one expects that the regular representation of ''G'' will decompose according to some kind of continuous spectrum, of representations involving a continuous parameter, as well as a discrete spectrum. The ''principal series'' representations are some induced representations constructed in a uniform way, in order to fill out the continuous part of the spectrum. In more detail, the unitary dual is the space of all representations relevant to decomposing the regular representation. The discrete series consists of 'atoms' of the unitary dual (points carrying a Plancherel measure > 0). In the earliest examples studied, the rest (or most) of the unitary dual could be parametrised by starting with a subgroup ''H'' of ''G'', simpler but not compact, and building up induced representations using represen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
