Deterministic Solution of the Discrete Wigner Equation

  • Johann CervenkaEmail author
  • Paul Ellinghaus
  • Mihail Nedjalkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8962)


The Wigner formalism provides a convenient formulation of quantum mechanics in the phase space. Deterministic solutions of the Wigner equation are especially needed for problems where phase space quantities vary over several orders of magnitude and thus can not be resolved by the existing stochastic approaches. However, finite difference schemes have been problematic due to the discretization of the diffusion term in this differential equation. A new approach, which uses an integral formulation of the Wigner equation that avoids the problematic differentiation, is shown here. The results of the deterministic method are compared and validated with solutions of the Schrödinger equation. Furthermore, certain numerical aspects pertaining to the demanded parallel implementation are discussed.


Discrete Wigner equation Integral formulation 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Johann Cervenka
    • 1
    Email author
  • Paul Ellinghaus
    • 1
  • Mihail Nedjalkov
    • 1
  1. 1.Institute for MicroelectronicsTU WienViennaAustria

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