Integration of quantum hydrodynamical equation

Vera G. Ulyanova; Andrey L. Sanin

doi:10.1117/12.726712

10 April 2007 Integration of quantum hydrodynamical equation

Vera G. Ulyanova, Andrey L. Sanin

Proceedings Volume 6597, Nanodesign, Technology, and Computer Simulations; 659709 (2007) https://doi.org/10.1117/12.726712
Event: Nanodesign, Technology, and Computer Simulations, 2006, Olsztyn, Poland

Abstract

Quantum hydrodynamics equations describing the dynamics of quantum fluid are a subject of this report (QFD).These equations can be used to decide the wide class of problem. But there are the calculated difficulties for the equations, which take place for nonlinear hyperbolic systems. In this connection, It is necessary to impose the additional restrictions which assure the existence and unique of solutions. As test sample, we use the free wave packet and study its behavior at the different initial and boundary conditions. The calculations of wave packet propagation cause in numerical algorithm the division. In numerical algorithm at the calculations of wave packet propagation, there arises the problem of division by zero. To overcome this problem we have to sew together discrete numerical and analytical continuous solutions on the boundary. We demonstrate here for the free wave packet that the numerical solution corresponds to the analytical solution.

Citation Download Citation

Vera G. Ulyanova and Andrey L. Sanin "Integration of quantum hydrodynamical equation", Proc. SPIE 6597, Nanodesign, Technology, and Computer Simulations, 659709 (10 April 2007); https://doi.org/10.1117/12.726712

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