Dirichlet problems for stationary von Neumann-Landau wave equations

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 Schrödinger's wave equation. In this paper, we concern with the Dirichlet problem of the stationary von Neumann-Landau wave equation: {(- \triangle_x + \triangle_y) Φ(x, y) = 0, x, y \in Ω, Φ|_{\partial Ω\times \partial Ω} = 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.

9 pages