Advertisement

Motion of vortex lines in quantum mechanics

  • Cezary Sliwa
  • Iwo Bialynicki-Birula
  • Zofia Bialynicka-Birula
  • Tomasz Mloduchowski
Conference paper
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 71)

Abstract

In quantum theory, vortex lines arise in the hydrodynamic interpretation of the wave equation. In this interpretation, which is originally due to Madelung, the flow of the probability density for a single particle is described in terms of the hydrodynamic variables. For the sake of simplicity, the standard time-dependent Schrödinger equation, and the related vortex lines embedded in the probability fluid of the quantum particle, are considered here. A vortex line in this case is simply the curve defined by equating the wave function to zero. The linearity of the Schrödinger equation enables us to obtain a large family of exact time-dependent analytic solutions for the wave functions with vortex lines. Moreover, the method is general enough to allow for various initial configurations of the vortex lines.

Although the equation of motion of the quantum mechanical probability fluid is different in its literal form from the equations describing the real physical fluid, we believe that the evolution of the vorticity in the quantum and in the real fluid share the same qualitative features that can be described in terms of the topology of the vortex lines configurations. The general phenomena such as the switch-over, creation and annihilation of vortices can be observed in the quantum mechanical fluid.

Keywords

Quantum Mechanic Vortex Line Quantum Particle Real Fluid Schrodinger Equation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Madelung, O. 1926, Z. Phys40, 342.Google Scholar
  2. Bialynicki-Birula, I., Bialynicka-Birula, Z. & Sliwa, C. 2000, Motion of vortex lines in quantum mechanics. Phys. Rev. A61, 032110.CrossRefADSGoogle Scholar
  3. Bialynicki-Birula, I., Mioduchowski, T., Radozycki, T. & Sliwa, C. 2001, Vortex lines in motion. Ada Phys. Pol.100 — Supplement, 29.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Cezary Sliwa
    • 1
  • Iwo Bialynicki-Birula
    • 1
  • Zofia Bialynicka-Birula
    • 2
  • Tomasz Mloduchowski
    • 3
  1. 1.Center for Theoretical PhysicsWarsawPoland
  2. 2.Institute of PhysicsWarsawPoland
  3. 3.S. I. Witkiewicz High SchoolWarsawPoland

Personalised recommendations