Decomposition Of Spectrum (functional Analysis)
In mathematics, especially functional analysis, the spectrum of an operator generalizes the notion of eigenvalues. Given an operator, it is sometimes useful to break up the spectrum into various parts. This article discusses a few examples of such decompositions.
Read more about Decomposition Of Spectrum (functional Analysis): Operators On Banach Space, Self Adjoint Operators On Hilbert Space
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Decomposition Of Spectrum (functional Analysis) - Self Adjoint Operators On Hilbert Space - Physics
... In quantum mechanics,observables are,not necessarily bounded,self adjoint operators and their spectra are the possible outcomes of measurements ... Absolutely continuous spectrumof a physical observable corresponds to free states of a system,while the pure point spectrumcorresponds to bound states ... The singular spectrumcorrespond to physically impossible outcomes ...
... In quantum mechanics,observables are,not necessarily bounded,self adjoint operators and their spectra are the possible outcomes of measurements ... Absolutely continuous spectrumof a physical observable corresponds to free states of a system,while the pure point spectrumcorresponds to bound states ... The singular spectrumcorrespond to physically impossible outcomes ...