Dirichlet problems for stationary von Neumann-Landau wave equations

Details Dirichlet problems for stationary von Neumann-Landau wave equations Dirichlet problems for stationary von Neumann-Landau wave equations

2007-05-25

arxiv.org/abs/0705.3685v1

Physics

Mathematical Physics

9 pages

Scientific paper

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 $\Omega$ is a bounded domain in $\mathbf{R}^n.$ 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.

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