Abstract
We study semiclassical approximations to the density matrix of a system of Fermions in a one body potential. We derive an expression for the propagator in terms of first and second derivatives of the potential. Our result is thus exact for a harmonic oscillator potential and is equivalent to a partial resummation of the Wigner-Kirkwoodh-expansion. It leads to densities which are well-defined also in the classically forbidden region.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Wigner, E.: Phys. Rev.40, 749 (1932)
Kirkwood, J.G.: Phys. Rev.44, 31 (1933)
Bhaduri, R.K., Ross, C.K.: Phys. Rev. Lett.27, 606 (1971)
Jennings, B.K.: Ph. D. Thesis, McMaster University, 1976
Bohigas, O., Campi, X., Krivine, H., Treiner, J.: Phys. Lett.64 B, 381 (1976)
Chu, Y.H., Jennings, B.K., Brack, M.: Phys. Lett.68 B, 407 (1977)
Jennings, B.K., Bhaduri, R.K., Brack, M.: Nucl. Phys. A253, 29 (1975) and Phys. Rev. Lett.34, 228 (1975)
Bhaduri, R.K.: Phys. Rev. Lett.39, 329 (1977)
Gumpertsberger, G., Schuck, P.: Phys. Lett.66 B, 219 (1977)
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions, fifth printing, NewYork: Dover 1968
Krivchenkov: Collected Problems in quantum mechanics, Ed. Ter Haar, D., London: Infosearch 1964
Voros, A.: Thèse d'Etat, Saclay 1977
Feynman, R.P., Hibbs, A.R.: Quantum Mechanics and Path Integral, NewYork: McGraw Hill 1965
Erdelyi, A. (Editor): Higher Transcendental Functions, Vol. II, NewYork: McGraw Hill, 1963; eqs. 8.5 (11) and 10.13 (22)
Strutinsky, V.M.: Nucl. Phys. A95, 420 (1967); A122, 1 (1968)
Brack, M., Damgaard, J., Jensen, A.S., Pauli, H.C., Strutinsky, V.M., Wong, C.Y.: Rev. Mod. Phys.44, 320 (1972)
Vautherin, D., Brink, D.M.: Phys. Rev. C5, 626 (1972); see also Negele, J.W., Vautherin, D.: Phys. Rev. C5, 1472 (1972), and ibid. C11, 1031 (1975)
Balazs, N., Zipfel, G.: Ann. Phys. (NewYork)77, 139 (1973); J. Math. Phys.15, 2086 (1974)
Balazs, N., Pauli, H.C.: Preprint Heidelberg, MPIH-1977-V9
Brack, M., Pauli, H.C.: Nucl. Phys. A207, 401 (1973)
Swiatecki, W.J.: Proc. Phys. Soc. (London) A65, 285 (1955)
Author information
Authors and Affiliations
Additional information
The authors are indebted to B.K. Jennings for very stimulating discussions.
Rights and permissions
About this article
Cite this article
Durand, M., Brack, M. & Schuck, P. A semiclassical density matrix valid beyond the classically allowed region. Z Physik A 286, 381–392 (1978). https://doi.org/10.1007/BF01408895
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01408895