AUTOKETs are the clever trick of quantum physicists!

Опубликовано: 25 Сентябрь 2026
на канале: YouSciences by GIUX

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Eigenkets are the clever trick of quantum physicists! In Quantitative Mechanics, eigenstates (eigenkets) play a key role. They are eigenvectors that define rays, which represent quantum states. Each Hermitian operator can be associated with a set of eigenvalues (spectrum) that capture the numerical information of these rays. Rays are also called eigenspaces. The stroke of genius consists in writing a generic state as a linear combination of these eigenkets relative to the associated operator. The advantage is seen by combining the spectral decomposition of the operator with the superposition of the state in the basis of the #eigenkets #eigenstates #ket #eigenstate #eigenspace #spectraltheorem #spectra #spectrum #quantummechanics #functionalanalysis #resolvent #physics #mathematics #geometry #physics #maths #vonneumann #matemáticas #doctorgiux #giux #yousciences

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Further reading:
https://it.wikipedia.org/wiki/Eugenstate
https://it.wikipedia.org/wiki/Hilbert...
https://it.wikipedia.org/wiki/Eigenve...
https://en.wikipedia.org/wiki/Spectra...

Quantum Mechanics Books:
➤John S. Townsend, A Modern Approach to Quantum Mechanics, Univ Science Books (2012)
➤Dirac, Paul A. M. The Principles of Quantum Mechanics. Paolo Boringhieri, Turin 1959 (1958).
➤J.J. Sakurai, Jim Napolitano, Modern Quantum Mechanics,
second edition, Zanichelli.
➤R.P. Feynman et al., Feynman's Physics, Volume III, Masson
➤L. Landau and E. Lifschitz, Quantum Mechanics, Editori Riuniti.
➤S. Gasiorowicz, Quantum Physics, J. Wiley & Sons.
➤Born, Max., Atomic Physics, Boringhieri 1968 BU Manual
➤Feynman, The Physics of, vol. 3, Quantum Mechanics, Zanichelli, Bologna 2001 - BU

Other materials:
➤https://dalfovo.science.unitn.it/lezi...
➤http://www.cs.infn.it/appunti/appunti...
➤https://www.eoinfnpr.it/Appunti_2015.pdf
➤Book collection: https://www.lfns.it/STORIA/Download/P...

Chapter summary
00:00 Overture:
01:10 Eigenkets
04:58 Distinguished Eigenvalues and Orthogonal Eigenkets
12:50 Degeneracy
16:50 Fourier Trick
20:32 Completeness Relation
23:11 Example: Parseval Identity

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