The classical limit of quantum mechanics and the Fejér sum of the Fourier series expansion of a classical quantity
- 1 January 1999
- journal article
- letter
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 32 (4) , L57-L62
- https://doi.org/10.1088/0305-4470/32/4/003
Abstract
In quantum mechanics, the expectation value of a quantity on a quantum state, provided that the state itself gives in the classical limit a motion of a particle in a definite path, in the classical limit goes over to a Fourier series form of the classical quantity. In contrast to this widely accepted point of view, a rigorous calculation shows that the expectation value on such a state in the classical limit exactly gives the Fejér arithmetic mean of the partial sums of the Fourier series.Keywords
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