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Weak quantization

Ehrenfest, Paul and Tolman, Richard C. (1924) Weak quantization. Physical Review, 24 (3). pp. 287-295. ISSN 0031-899X.

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Quantization is called weak when a motion apparently allowed by the equation ∫pdq=nh, has less than the normal a-priori weight. It is believed that the deficiency in a-priori weight is taken over, either by neighboring classically allowed motions, or by neighboring strongly quantized motions when such are present in the region of the phase-space considered. Weak quantization is to be expected when uncertainties arise as to the period that should be used in determining the limits of the phase integral ∫pdq. Several cases are considered; (a) when the period is so long that there is considerable chance of interruption by a quantum transition; (b) when a system has two apparent periods, a long true period T and a short quasi-period θ; (c) when the periodicity is disturbed frequently in a fortuitous manner as by molecular collisions. In case (b), the tendency towards quantization with respect to T may be gradually replaced by quantization with respect to θ as T is lengthened, and then the probability of quantum transitions which correspond to quantization with respect to T is weakened while that of transitions related to θ is strengthened. This suggests the possibility that the strengthening of the probability of transitions related to a period θ may be accompanied by a strengthening of quantization with respect to that period.

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Additional Information:©1924 The American Physical Society. Received April 1924.
Issue or Number:3
Record Number:CaltechAUTHORS:EHRpr24
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5505
Deposited By: Tony Diaz
Deposited On:20 Oct 2006
Last Modified:02 Oct 2019 23:23

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