Anyone who has read or studied quantum mechanics will surely have been struck by the futuristic and modern notation typical of this mysterious theory. This notation, which uses particular symbols such as 〈X|Y〉, is due to the physicist Paul Dirac, who introduced it in the late 1920s to formalize the mathematics of quantum mechanics. This video reveals the power of the quantum bracket, which represents the connection between the space of |kets〉 and its dual space of 〈bras| . It turns out that bras are functionals that map the |kets〉 to scalars via an inner product. This explains why this formalism is used. #bracket #ket #autoket #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/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
00:58 The Dual Space of Brackets
06:06 Functionals
07:58 The Dirac Bracket
10:44 Square norm
12:50 The Bra as a straightedge
15:26 Hermitian torsion
18:20 Exercise: normalization of a ket
Executive Production by Giux