Quantentheorie in hydrodynamischer Form

  title={Quantentheorie in hydrodynamischer Form},
  author={Erwin Madelung},
  journal={Zeitschrift f{\"u}r Physik},
  • E. Madelung
  • Published 1 March 1927
  • Physics
  • Zeitschrift für Physik
ZusammenfassungEs wird gezeigt, daß man die Schrödingersche Gleichung des Einelektronen-problems in die Form der hydrodynamischen Gleichungen transformieren kann. 
Madelung, Gross-Pitaevskii and Korteweg
This paper surveys various aspects of the hydrodynamic formulation of the nonlinear Schrodinger equation obtained via the Madelung transform in connection to models of quantum hydrodynamics and to
Time-Independent Schrödinger and Riccati Equations
In Sect. 2.11 it has been shown how a generalization of the creation and annihilation operators, known from the algebraic treatment of the harmonic oscillator (HO) problem.
Integrable Substructure in a Korteweg Capillarity Model. A Karman-Tsien Type Constitutive Relation
A classical Korteweg capillarity system with a Karman-Tsien type (κ, ρ) constitutive relation is shown, via a Madelung transformation and use of invariants of motion, to admit integrable Hamiltonian
Morphing quantum mechanics and fluid dynamics
We investigate the effects of given pressure gradients on hydrodynamic flow equations. We obtain results in terms of implicit solutions and also in the framework of an extra-dimensional formalism
q-Gaussian integrable Hamiltonian reductions in anisentropic gasdynamics
Integrable reductions in non-isothermal spatial gasdynamics are isolated corresponding to q-Gaussian density distributions. The availability of a Tsallis parameter q in the reductions permits the
Dissipative quantum mechanics. Metriplectic dynamics in action
The inherent linearity of quantum mechanics is one of the difficulties in developing a fully quantum theory of dissipative processes. Several microscopic and more or less phenomenological
A Physical Axiomatic Approach to Schrodinger's Equation
The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the
Markovian limits of dissipative field dynamics
SummaryMarkovian limits of the field equation of dissipative field dynamics are discussed and compared with the field equation of small-amplitude fluid dynamics for nonsolenoid velocity fields and of