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Zwiebach obtained his Ph.D. in 1983, working under the supervision of Murray Gell-Mann. He has held postdoctoral positions at the University of California, Berkeley , and at the Massachusetts Institute of Technology , where he became an assistant professor of physics in 1987, and a permanent member of the faculty in 1994.
Classifying these particles led him to propose that a quantum number, called strangeness, would be conserved by the strong and the electromagnetic interactions, but not by the weak interaction. [43] Another of Gell-Mann's ideas is the Gell-Mann–Okubo formula, which was, initially, a formula based on empirical results, but was later explained ...
In double field theory, the T-duality transformation of exchanging momentum and winding modes of closed strings on toroidal backgrounds translates to a generalized coordinate transformation on a doubled spacetime, where one set of its coordinates is dual to momentum modes and the second set of coordinates is interpreted as dual to winding modes of the closed string.
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot.
The probability that the quantum particle will be found in the classically forbidden region is small. In the classically allowed region, meanwhile, the probability the quantum particle will be found in a given interval is approximately the fraction of time the classical particle spends in that interval over one period of motion. [17]
Probability amplitudes provide a relationship between the quantum state vector of a system and the results of observations of that system, a link was first proposed by Max Born, in 1926. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics.
The Elitzur–Vaidman bomb-tester is a quantum mechanics thought experiment that uses interaction-free measurements to verify that a bomb is functional without having to detonate it. It was conceived in 1993 by Avshalom Elitzur and Lev Vaidman. Since their publication, real-world experiments have confirmed that their theoretical method works as ...
In quantum mechanics, a complete set of commuting observables (CSCO) is a set of commuting operators whose common eigenvectors can be used as a basis to express any quantum state. In the case of operators with discrete spectra, a CSCO is a set of commuting observables whose simultaneous eigenspaces span the Hilbert space and are linearly ...