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Abstract: It is known that von Neumann-Landau wave equation can present a mathematicalformalism of motion of quantum mechanics, that is an extension ofSchr\-{o}dinger-s wave equation. In this paper, we concern with the Dirichletproblem 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 abounded domain in $\mathbf{R}^n.$ By introducing anti-inner product spaces, weshow the existence and uniqueness of the generalized solution for the aboveDirichlet problem by functional-analytic methods.



Autor: Zeqian Chen

Fuente: https://arxiv.org/







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