MATRICES in Quantum Mechanics
The matrices of quantum mechanics are tables made of rows and columns that form a new, so-called noncommutative algebra. It was Werner Heisenberg who glimpsed this mysterious world, lost alone on the tiny island of Heligoland in the 1920s. Every quantum operator, every state vector, every dual of Hilbert space is represented by a matrix, either a column vector or a row. In this representation, our abstract objects find a more concrete and computable algebraic form. Furthermore, the Hermitian operators associated with observables, when expressed in the basis of relative eigenkets, become diagonal matrices! #matrices #eigenket #eigenstates #ket #eigenstate #eigenspace #quantummechanics #vectors #tensors #physics #mathematics #geometry #physics #maths #vonneumann #mathematics #doctorgiux #giux #yousciences
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Further reading:
https://it.wikipedia.org/wiki/Eigenstate
https://it.wikipedia.org/wiki/Spazio_...
https://it.wikipedia.org/wiki/Eigenve...
https://en.wikipedia.org/wiki/Spectra...
Mechanics Books Quantum Mechanics:
➤John S. Townsend, A Modern Approach to Quantum Mechanics, University 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
01:05 Representative Matrix
04:15 Additive Matrix
05:40 Product Matrix
09:23 Heartless fix
09:45 Ket column
12:50 Bra row
14:28 Scalar Product
16:25 Representation Diagonal
10.45pm Final
Executive Production by Giux