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The Classical Limit of Quantum Mechanics and the Fejer Sum of the Fourier Series Expansion of a Classical Quantity

Q. H. Liu
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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 classical limit goes over to 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 classical limit exactly gives the Fejér's arithmetic mean of the partial sums of the Fourier series.

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Q. H. Liu. 2000-08-01. The Classical Limit of Quantum Mechanics and the Fejer Sum of the Fourier Series Expansion of a Classical Quantity. https://doi.org/10.1088/0305-4470%2F32%2F4%2F003

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