Solution of the Time Dependent Schrödinger Equation and the Advection Equation via Quantum Walk with Variable ParametersReport as inadecuate




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We propose a solution method of Time Dependent Schr?dinger EquationTDSE and the advection equation by quantum walk-quantumcellular automaton with spatially or temporally variable parameters. Usingnumerical method, we establish the quantitative relation between the quantumwalk with the space dependent parameters and the -Time DependentSchr?dinger Equation with a space dependent imaginary diffusion coefficient- or-the advection equation with space dependent velocity fields-. Using the4-point-averaging manipulation in the solution of advection equation by quantumwalk, we find that only one component can be extracted out of two components ofleft-moving and right-moving solutions. In general it isnot so easy to solve an advection equation without numerical diffusion, butthis method provides perfectly diffusion free solution by virtue of itsunitarity. Moreover our findings provide a clue to find more general spacedependent formalisms such as solution method of TDSE with space dependentresolution by quantum walk.

KEYWORDS

Quantum Walk; Quantum Cellular Automaton; Time Dependent Schrödinger Equation; Advection Equation

Cite this paper

S. Hamada, M. Kawahata and H. Sekino -Solution of the Time Dependent Schrödinger Equation and the Advection Equation via Quantum Walk with Variable Parameters,- Journal of Quantum Information Science, Vol. 3 No. 3, 2013, pp. 107-119. doi: 10.4236-jqis.2013.33015.





Author: Shinji Hamada, Masayuki Kawahata, Hideo Sekino

Source: http://www.scirp.org/



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