Solution of the quantum fluid dynamical equations with radial basis function interpolation

The paper proposes a numerical technique within the Lagrangian description for propagating the quantum fluid dynamical (QFD) equations in terms of the Madelung field variables R and S, which are connected to the wave function via the transformation Psi= exp{(R + iS)/(h) over bar}. The technique rest s on the QFD equations depending only on the form, not the magnitude, of th e probability density rho = \psi\(2) and on the structure of R = (h) over b ar/2 In rho generally being simpler and smoother than rho. The spatially sm ooth functions R and S are especially suitable for multivariate radial basi s function interpolation to enable the implementation of a robust numerical scheme. Examples of two-dimensional model systems show that the method riv als, in both efficiency and accuracy, the split-operator and Chebychev expa nsion methods. The results on a three-dimensional model system indicates th at the present method is superior to the existing ones, especially, for its low storage requirement and its uniform accuracy. The advantage of the new algorithm is expected to increase fur higher dimensional systems to provid e a practical computational tool.