Abstract
We show that the spread of momentum can be broken up into two terms, one that depends only on the change in amplitude and the other which depends only on the deviations of current from the average momentum. We present a method for measuring the relative contributions of each and interpret each contribution in terms of local quantities. A generalization for arbitrary operators is given. For the case of the Hamiltonian, the local value of energy is shown to yield the quantum potential as defined by Bohm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Bohm,Phys. Rev. 85, 166 (1952).
In the case where the variables are time and frequency variations of this equation has been derived by J. Ville,Cables Transm. 2A, 61 (1948); L. M. Fink, translated inProblems Inf. Transm. 2, 11 (1966); L. Mandel,Am. J. Phys. 42, 840 (1974).
L. Cohen and C. Lee, inAdvanced Algorithms and Architectures for Signal Processing III, Franklin T. Luk, ed.;Proc. SPIE 975, 186 (1988); L. Cohen and C. Lee,Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing 3, 2451 (1990).
L. Cohen,IEEE Proc. 77, 941 (1989).
E. Merzbacher,Quantum Mechanics (Wiley, New York, 1970).
L. Cohen and C. Lee,Found. Phys. 17, 561 (1987).
E. P. Wigner,Phys. Rev. 40, 749 (1932).
M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner,Phys. Rep. 106, 121 (1984).
L. Cohen,J. Math. Phys. 7, 781 (1966).
Author information
Authors and Affiliations
Additional information
It is a pleasure to dedicate this paper to John Bell in honor of his 60th birthday.
This work is supported in part by The City University Research Award Program.
Rights and permissions
About this article
Cite this article
Cohen, L. Momentum spread: Amplitude and current contributions. Found Phys 20, 1455–1473 (1990). https://doi.org/10.1007/BF01883518
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01883518