Abstract
We consider a Hermitian operator L̂. The mean value of the operator is, as we know, defined as
.
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Biographical Notes
Ehrenfest, Paul, Austrian physicist, *Wien 18.1.1880, † Leiden 25.9.1933. E. was a professor in Leiden (Netherlands) from 1912 on. He contributed to atomic physics with his hypothesis of adi-abatic invariants (BR).
Poisson, Siméon Denis, French mathematician, *Pithiviers 21.6.1781, † Paris 25.4.1840. P. was a student of the École Polytechnique and he was employed there after completing his studies, being a professor from 1802. P. was a member of the bureau of lengths and of the Académie des Sciences. He was a French peer from 1837. P. worked in many fields, e.g. general mechanics, heat conduction, potential theory, differential equations and the calculus of probabilities.
Poincaré, Henri, French mathematician, *Nancy 29.4.1854, † Paris 17.7.1912. P. studied at the Ecole Polytechnique and became professor at Caen in 1879, later, at Paris. He produced more than 30 books. At the turn of the century he was believed to be the outstanding mathematician of his age. P.’s greatest contribution to mathematical physics was a paper on the dynamics of the electron (1906) in which he obtained, independently of Einstein, many of the results of special relativity. Einstein developed the theory from elementary considerations about light signalling, whereas P.’s treatment was based on the theory of electromag-netism and was thus restricted. P.’s writings on the philosophy of science were as important as his contributions to mathematics. He became a member of the Académie Francaise in 1908 (taken from Encyclopedia Britannica, 1960 edition).
Lagrange, Joseph Louis, French mathematician, *Torino 25.1.1736, † Paris 10.4.1813. L. came from a French-Italian family, and in 1755 became professor in Torino. In 1766 he went to Berlin as the director of the mathematical-physical class of the academy. In 1786, after the death of Frederick II, he went to Paris, where he considerably supported the reform of the measuring system, and where he was professor at several universities. His very extensive work contains a new foundation of variational calculus (1760) and its application to dynamics, contributions to the three-body problem (1772), the application of the theory of chain fractions to the solution of equations (1767), number-theoretical problems, and an unsuccessful reduction of infinitesimal calculus to algebra. With his “Mécanique analytique” (1788), L. became the initiator of analytic mechanics. Important for function theory is his “Théorie des fonctions analytiques, contenant les principes du calcul différentiel” (1789), and for algebra his “Traité de la résolution des équations numériques de tous degrés (1798).
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© 1993 Springer-Verlag Berlin Heidelberg
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Greiner, W. (1993). The Transition from Classical to Quantum Mechanics. In: Quantum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-30374-0_8
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DOI: https://doi.org/10.1007/978-3-662-30374-0_8
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