Structure of the Wave Function of Crystalline 4He

  • S. A. Vitiello
  • K. J. Runge
  • M. H. Kalos
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 33)


The nature of the wave function for quantum crystals has been an outstanding problem for some time. Although a Jastrow product wave function gives a qualitatively correct description of the liquid, and although such a wave function can describe a crystal, the result is in serious disagreement with experiment. The standard treatment is to construct a lattice and directly couple the particles to its sites. Although this gives fair numerical agreement with some crystal properties, it is at the expense of breaking the Bose symmetry of the crystal. We introduce here a new class of trial wave functions that are symmetric under particle exchange. They give a lower variational energy than, and have properties comparable with those given by trial functions in which atoms are explicitly localized.


Wave Function Trial Function Triangular Lattice Real Particle Trial Wave Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. P. Hansen and D. Levesque, Phys. Rev. 165, 293 (1968).ADSCrossRefGoogle Scholar
  2. 2.
    L. H. Nosanow, Phys. Rev. Lett. 13, 270 (1964).ADSCrossRefGoogle Scholar
  3. 3.
    We are concerned here with systems obeying periodic boundary conditions. In this case it can be shown that the true ground state wave function is translationally invariant even in the solid phase.Google Scholar
  4. 4.
    Silvio Vitiello, Karl Runge and M. H. Kalos, Phys. Rev. Lett. 60, 1970 (1988).ADSCrossRefGoogle Scholar
  5. 5.
    R. P. Feynman, Statistical Mechanics, W. A. Benjamin, Inc., Reading, 1972.Google Scholar
  6. 6.
    K. Schmidt, M. H. Kalos, M. A. Lee and G. V. Chester, Phys. Rev. Lett. 45, 573 (1980).ADSCrossRefGoogle Scholar
  7. 7.
    N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, J. Chem. Phys. 21, 1087 (1953).ADSCrossRefGoogle Scholar
  8. 8.
    R. A. Aziz, V. P. S. Nain, J. S. Carley, W. L. Taylor and G. T. McConville, J. Chem. Phys. 70, 4330 (1970).ADSCrossRefGoogle Scholar
  9. 9.
    W. L. McMillan, Phys. Rev. 138, A442 (1965).ADSCrossRefGoogle Scholar
  10. 10.
    M. H. Kalos and P. A. Whitlock, Monte Carlo Methods, John Wiley & Sons, New York, 1986.MATHCrossRefGoogle Scholar
  11. 11.
    J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, Academic Press, London, 1976.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • S. A. Vitiello
    • 1
  • K. J. Runge
    • 1
  • M. H. Kalos
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

Personalised recommendations