Rigged Hilbert spaces provide the mathematical foundation for continuous spectra in quantum mechanics.
Rigged Hilbert spaces provide the mathematical framework necessary to properly formulate continuous spectra and generalized eigenstates in quantum mechanics.
The provided literature clearly supports the premise that rigged Hilbert spaces are used to mathematically handle continuous spectra and generalized eigenfunctions in quantum mechanics, such as in the study of resonances, Gamow states, and quantum optical phase operators.
Gadella M, Fortín S, Jorge JP, Losada M. Mathematical Models for Unstable Quantum Systems and Gamow States.. 2022. https://doi.org/10.3390/e24060804
Discusses how Gamow states, representing resonances and continuous spectra, are formulated as vectors in extensions of Hilbert spaces known as rigged Hilbert spaces.
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Matthew J. Colbrook, Andrew Horning, Tianyiwa Xie. Computing Generalized Eigenfunctions in Rigged Hilbert Spaces. 2024. https://doi.org/10.48550/arXiv.2410.08343
Presents a computational scheme for generalized eigenfunctions of self-adjoint operators with continuous spectra using rigged Hilbert spaces.
Bordon K, Vaccaro JA. Quantum optical phase, rigged Hilbert spaces and complementarity.. 2024. https://doi.org/10.1098/rsta.2023.0328
Explains how an extended rigged Hilbert space supports strong limits of phase operators and includes their continuous or generalized eigenstates.
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