English

Dirichlet problems for stationary von Neumann-Landau wave equations

Mathematical Physics 2007-05-28 v1 math.MP

Abstract

It is known that von Neumann-Landau wave equation can present a mathematical formalism of motion of quantum mechanics, that is an extension of Schr\"{o}dinger's wave equation. In this paper, we concern with the Dirichlet problem of the stationary von Neumann-Landau wave equation: {(- \triangle_x + \triangle_y) \Phi (x, y) = 0, x, y \in \Omega, \Phi|_{\partial \Omega \times \partial \Omega} = f, where Ω\Omega is a bounded domain in Rn.\mathbf{R}^n. By introducing anti-inner product spaces, we show the existence and uniqueness of the generalized solution for the above Dirichlet problem by functional-analytic methods.

Keywords

Cite

@article{arxiv.0705.3685,
  title  = {Dirichlet problems for stationary von Neumann-Landau wave equations},
  author = {Zeqian Chen},
  journal= {arXiv preprint arXiv:0705.3685},
  year   = {2007}
}
R2 v1 2026-06-21T08:31:52.807Z