What are our limits in seeing the infinitely small: What are Observables?
To observe and/or measure in quantum mechanics means to alter, disturb, or even destroy what we are observing! This mysterious effect of the infinitely small world is the seed of quantum mechanics. During the creation of quantum mechanics, physicists invented a mechanism to mathematically describe this phenomenon through objects called observables. An observable is nothing more than a Hermitian algebraic operator acting in the space of kets (i.e., states); and, like a function y = f(x), it associates another ket (state); But these states are not just any states, but those that satisfy a particular eigenvalue equation. #observables #operators #Hermitian #bracket #ket #eigenket #states #quantummechanics #physics #mathematics #Hilbert #spacevector #quantum #geometry #mathematics #linearalgebra #linearalgebra #vectors #matrix #operators #quantumstates #vectors #dirachannel
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Further reading:
https://it.wikipedia.org/wiki/Osserva...
https://it.wikipedia.org/wiki/Operato...)
https://it.wikipedia.org/wiki/Notazio...
https://it.wikipedia.org/wiki/Spazio_...
https://it.wikipedia.org/wiki/Forma_s...
https://it.wikipedia.org/wiki/Spazio_...
https://en.wikipedia.org/wiki/Bra%E2%...
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: The quantum cat
01:06 Observables
04:55 Measurement, Collapse, Eigenstates
07:02 Operators
11:10 Linear operators
12:50 Operators in Bra space
14:28 Adjunct operator
15:15 Operator Hermitian
5:26 PM Operators' Product
7:56 PM Exercise: Adding the Product
Executive Production by Giux