1994
DOI: 10.1103/physreva.50.2854
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Abstract: The classical limit of quantum mechanics is usually discussed in terms of Ehrenfest*s theorem, which states that, -for a sufficiently narrow wave packet, the mean position in the quantum state will follow a classical trajectory. We show, however, that that criterion is neither necessary nor sufficient to identify the classical regime. Generally speaking, the classical limit of a quantum state is not a single classical orbit, but an ensemble of orbits. The failure of the mean position in the quantum state to fo… Show more

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Cited by 157 publications
(149 citation statements)
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“…The study of chaos in quantum dynamics has led to differing views on the conditions required for demonstrating quantum-classical correspondence [1,2]. Moreover, the criteria by which this correspondence should be measured have also been a subject of some controversy [3][4][5].…”
Section: Introductionmentioning
confidence: 99%
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“…The study of chaos in quantum dynamics has led to differing views on the conditions required for demonstrating quantum-classical correspondence [1,2]. Moreover, the criteria by which this correspondence should be measured have also been a subject of some controversy [3][4][5].…”
Section: Introductionmentioning
confidence: 99%
“…Moreover, the criteria by which this correspondence should be measured have also been a subject of some controversy [3][4][5]. While much of the earlier work on this topic is concerned with characterizing the degree of correspondence between quantum expectation values and classical dynamical variables [6][7][8], the more recent approach is to focus on differences between the properties of quantum states and associated classical phase space densities evolved according to Liouville's equation [1,[9][10][11][12][13].…”
Section: Introductionmentioning
confidence: 99%
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“…Ho wever, as i t has been p oi nted out by Ba l lenti ne and col l abora to rs, see R ef. [3], i n most of the cases of the cl assical l i mit of qua ntum m echani cs we wi l l face pro bl ems where condi ti on (1 .10) i s sati sÙed, but condi ti ons (1 .3) and (1 .4) are no t. Such circum sta nces signi fy tha t the classical l i m it of the qua ntum state i n questi on wi l l b e an ensembl e of classical tra j ectori es.…”
Section: E H R En Fe St T H Eo R Em Smentioning
confidence: 99%
“…In other cases, such as the infinite well and infinite step potentials, verification is problematic [8][9][10][11]. Although the Ehrenfest theorem provides a (formal) general relationship between classical and quantum dynamics, it does not necessarily (neither sufficiently) characterize the classical regime [12]. Certainly, using only the aforementioned theorem, one cannot state that the mean values ⟨x⟩(t) and ⟨p⟩(t) are always equal to the functions x(t) and p(t); however, this statement does hold true in the limit n → ∞ (for a general discussion of the behaviour of a physical quantity for high values of the quantum number n, see, for example, Ref.…”
Section: Introductionmentioning
confidence: 99%