Abstract
Some wave functions separate into two or more distinct regions in phase space. Each region is characterized by a trajectory and a spread about that trajectory. The trajectory is the quantum mechanical current. We show that these regions correspond to parts of the wave function and that these parts are generally nonorthogonal.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Boashash, “Time-Frequency Signal Analysis,” inAdvances in Spectral Analysis, S. Haykin, ed. (Prentice-Hall, New Jersey, 1990).
H. I. Choi and W. J. Williams, “Improved time-frequency representation of multi-component signals using exponential kernels,”IEEE Trans. Acoust. Speech Signal. Process. 37(6), 862–871 (1989).
L. Cohen,IEEE Proc. 77, 941 (1989).
Y. Zhao, L. E. Atlas, and R. J. Marks II, “The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals,”IEEE Trans. Acoust. Speech Signal. Process. 38(7), 1084–1091 (1990).
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, “Instantaneous mean quantities in time-frequency analysis,”Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., pp. 2188–2191 (1988).
L. Cohen and C. Lee, “Instantaneous bandwidth,” inTime-Frequency Signal Analysis—Methods and Applications, B. Boashash, ed. (Longman-Cheshire, Wiley, 1992).
L. Cohen and C. Lee, “Instantaneous bandwidth for signals and spectrogram,”Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., pp. 2451–2454 (1990).
L. Cohen, “What is a Multicomponent Signal,”Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., pp. 113–116 (1992).
L. Cohen,Found. Phys. 20, 1455 (1990).
L. Cohen, “An equation for the uncertainty of an operator and its interpretation in terms of local values,” inFound. of Quant. Mech., T. D. Black,et al., eds. (World Scientific, Singapore, 1992), to appear.
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).
V. V. Kuryshkin,Int. J. Theor. Phys. 7, 451 (1972).
V. V. Kuryshkin and Yu. I. Zaparovanny,C. R. Acad. Sci. (Paris) 2, 17, 1984.
V. V. Kuryshkin, I. A. Lybas, and Yu. I. Zaparovanny,Ann. Fond. L. de Broglie 5, 105 (1980).
E. E. Entralgo, V. V. Kuryshkin, and Yu. I. Zaparovanny, inMicrophysical Reality and Quantum Formalism, A. van der Merweet al., eds. (Kluwer Academic, Dordrecht, 1988).
N. D. Cartwright,Physica 83A, 210 (1976).
R. F. O'Connell and E. P. Wigner,Phys. Lett. 85A, 121 (1981).
K. Wodkiewicz,Phys. Rev. Lett. 52, 1064 (1984).
Author information
Authors and Affiliations
Additional information
My interest in physics was inspired, as an undergraduate, by the remarkable books of Henry Margenau, particularlyFoundations of Physics andThe Mathematics of Physics and Chemistry. I never imagined then that I would have the good forture of being his student. It is a pleasure and an honor to dedicate this article to him as a small expression of my deep appreciation.
Rights and permissions
About this article
Cite this article
Cohen, L. Multipart wave functions. Found Phys 22, 691–711 (1992). https://doi.org/10.1007/BF01889673
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01889673