Acta mathematica scientia, Series B >
DIRICHLET PROBLEMS FOR STATIONARY VON NEUMANN-LANDAU WAVE EQUATIONS
Received date: 2007-05-28
Online published: 2009-09-20
Supported by
Supported partially by the National Natural Science Foundation of China (10775175)
In this article, we are concerned with the Dirichlet problem of the stationary von Neumann--Landau wave equation: { ( -Δx + Δy ) Φ (x, y) = 0, x, y ∈ Ω
Φ | ∂Ω×∂Ω = f,
where Ω is a bounded domain in Rn. 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.
Key words： von Neumann Landau equation; wave functions; Dirichlet problem
CHEN Ze-Qan . DIRICHLET PROBLEMS FOR STATIONARY VON NEUMANN-LANDAU WAVE EQUATIONS[J]. Acta mathematica scientia, Series B, 2009 , 29(5) : 1225 -1232 . DOI: 10.1016/S0252-9602(09)60099-0
[1] Bognär J. Indefinite Inner Product Spaces. Berlin: Springer-Verlag, 1974
[2] Chen Z. von Neumann--Landau equation for wave functions, wave-particle duality and collapses of wave functions. quant-ph/0703204, 2007
[3] Dirac P A M. The Principles of Quantum Mechanics. Fourth ed. Oxford: Oxford University Press, 1958
[4] Fan H Y, Li C. Invariant ``eigen-operator'' of the square of Schrödinger operator for deriving energy-level gap.
Phys Lett A, 2004, 321: 75--78
[5] John F. Partial Differential Equations. Fourth ed. New York: Springer-Verlag, 1982
[6] Landau L D and Lifshitz E M. Quantum Mechanics-Non-relativistic Theory. Third ed. Oxford: Pergamon Press, 1977
[7] von Neumann J. Mathematical Foundations of Quantum Mechanics. Princeton: Princeton University Press, 1955
[8] Reznik B. Unitary evolution between pure and mixed states. Phys Rev Lett, 1996, 76: 1192--1195
/
| 〈 |
|
〉 |