Wave function

In quantum mechanics, a wave function (or wavefunction) is a complex number complex-valued mathematical entity, or formalism, that describes the quantum state of an isolated Quantum mechanics quantum system. Quotes … what is the wave function? Is it a complete and comprehensive representation of the world? Or do we need additional physical quantities to fully capture reality, as Albert Einstein and others suspected? Or does the wave function have no direct connection with reality at all, merely characterizing our personal ignorance about what we will eventually measure in our experiments?Until physicists definitively answer these questions, they can’t really be said to understand quantum mechanics — thus Feynman’s lament. Which is bad, because quantum mechanics is the most fundamental theory we have, sitting squarely at the center of every serious attempt to formulate deep laws of nature. If nobody understands quantum mechanics, nobody understands the universe. Sean M. Carroll, https://www.nytimes.com/2019/09/07/opinion/sunday/quantum-physics.htm Even Physicists Don’t Understand Quantum Mechanics. Worse, they don’t seem to want to understand it. September 7, 2019 New York Times What is the empirical content of quantum mechanics? Or how does the wave function assigned to a physical system relate to the results of measurements on the system? The well-known connection rule is the Born rule, which has been precisely tested by experiments. It says that a (projective) measurement of an observable A on a system with the wave function |ψ⟩ will randomly obtain one of the Eigenvalues and eigenvectors eigenvalues of A, and the probability of obtaining an eigenvalue ai is given by |⟨ai|ψ⟩|2, where |ai⟩ is the Quantum state eigenstate corresponding to the eigenvalue ai. Shan Gao The Meaning of the Wave Function: In Search of the Ontology of Quantum Mechanics 2016 arXiv:1611.02738 [quant-ph] https://arxiv.org/abs/1611.02738 (199 pages, 8 figures. Draft of book published in 2017 by Cambridge University Press; quote from p. 6) text at books.google.com ... Pauli's exclusion principle was formalized by a number of authors ... as the requirement that the wave function of a multi-electron system is Dichromatic symmetry antisymmetric in the coordinates, Orbital hybridisation orbital and Spin (physics) spin, of all the electrons. This principle was incorporated into statistical mechanics by Enrico Fermi ... and Dirac, ... and for this reason particles obeying the exclusion principle are generally called 'fermions,' just as particles like photons for which the wave function is symmetric and which obey the statistics of Bose and Einstein are called 'bosons.' Steven Weinberg, The Quantum Theory of Fields, Volume 1: Foundations pbk reprint of 1995 1st vol. 1 of 2-volume set 9780521585552 Cambridge University Press 2005 9780521550017 https://books.google.com/books?id=doeDB3_WLvwC&pg=PA11 11–12 (609 pages) Quantum Theory of Fields, Vol. 2: Modern Applications External links Category:Quantum mechanics