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Journal of Chemical Physics / Volume 136 / Issue 3 / COMMUNICATIONS
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J. Chem. Phys. 136, 031102 (2012); http://dx.doi.org/10.1063/1.3680558 (4 pages)

Communication: Quantum mechanics without wavefunctions

Jeremy Schiff1 and Bill Poirier2

1Department of Mathematics, Bar-Ilan University, Ramat Gan 52900, Israel
2Department of Chemistry and Biochemistry, Texas Tech University, Box 41061, Lubbock, Texas 79409-1061, USA and Department of Physics, Texas Tech University, Box 41051, Lubbock, Texas 79409-1051, USA

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(Received 22 November 2011; accepted 11 January 2012; published online 19 January 2012)

We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications—theoretical, computational, and interpretational—are discussed.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THE 1D TIME-INDEPENDENT CASE
  3. THE 1D TIME-DEPENDENT CASE
  4. THE MANY-D TIME-DEPENDENT CASE
  5. CONCLUDING REMARKS

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KEYWORDS and PACS

Keywords

wave functions

PACS

  • 03.65.Ge

    Solutions of wave equations: bound states

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3680558

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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  6. M. F. González, X. Giménez, J. González, and J. M. Bofill, J. Math. Chem. 43, 350 (2008).
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  8. A. Bouda, Int. J. Mod. Phys. A 18, 3347 (2003).
  9. P. Holland, Ann. Phys. 315, 505 (2005).
  10. P. Holland, Proc. R. Soc. London, Ser. A 461, 3659 (2005).
  11. G. Parlant, Y.-C. Ou, K. Park, and B. Poirier, “Classical-like trajectory simulations for accurate computation of quantum reactive scattering probabilities,” Comput. Theor. Chem. (in press).
  12. D. Babyuk and R. E. Wyatt, J. Chem. Phys. 124, 214109 (2006)JCPSA6000124000021214109000001. [MEDLINE]

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