TY - JOUR

T1 - Solution of two-dimensional linear and nonlinear unsteady schrödinger equation using "quantum hydrodynamics" formulation with a mlpg collocation method

AU - Loukopoulos, V. C.

AU - Bourantas, G. C.

PY - 2014

Y1 - 2014

N2 - A numerical solution of the linear and nonlinear time-dependent Schrödinger equation is obtained, using the strong form MLPG Collocation method. Schrödinger equation is replaced by a system of coupled partial differential equations in terms of particle density and velocity potential, by separating the real and imaginary parts of a general solution, called a quantum hydrodynamic (QHD) equation, which is formally analogous to the equations of irrotational motion in a classical fluid. The approximation of the field variables is obtained with the Moving Least Squares (MLS) approximation and the implicit Crank-Nicolson scheme is used for time discretization. For the two-dimensional nonlinear Schrödinger equation, the lagging of coefficients method has been utilized to eliminate the nonlinearity of the corresponding examined problem. A Type-I nodal distribution is used in order to provide convergence for the discrete Laplacian operator used at the governing equation. Numerical results are validated, comparing them with analytical and numerical solutions.

AB - A numerical solution of the linear and nonlinear time-dependent Schrödinger equation is obtained, using the strong form MLPG Collocation method. Schrödinger equation is replaced by a system of coupled partial differential equations in terms of particle density and velocity potential, by separating the real and imaginary parts of a general solution, called a quantum hydrodynamic (QHD) equation, which is formally analogous to the equations of irrotational motion in a classical fluid. The approximation of the field variables is obtained with the Moving Least Squares (MLS) approximation and the implicit Crank-Nicolson scheme is used for time discretization. For the two-dimensional nonlinear Schrödinger equation, the lagging of coefficients method has been utilized to eliminate the nonlinearity of the corresponding examined problem. A Type-I nodal distribution is used in order to provide convergence for the discrete Laplacian operator used at the governing equation. Numerical results are validated, comparing them with analytical and numerical solutions.

KW - MLPG collocation method

KW - Moving least squares

KW - Quantum hydrodynamics

KW - Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=84923666867&partnerID=8YFLogxK

U2 - 10.3970/cmes.2014.103.049

DO - 10.3970/cmes.2014.103.049

M3 - Article

AN - SCOPUS:84923666867

SN - 1526-1492

VL - 103

SP - 49

EP - 70

JO - CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES

JF - CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES

IS - 1

ER -