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Quantum Algorithms

Wronskian method and the Schrödinger eigenvalue march

arXiv
Authors: Francisco M. Fernández

Year

2011

Paper ID

29081

Status

Preprint

Abstract Read

~2 min

Abstract Words

103

Citations

N/A

Abstract

We compare the Wronskian method (WM) and the Schrödinger eigenvalue march or canonical function method (SEM--CFM) for the calculation of the energies and eigenfunctions of the Schrödinger equation. The Wronskians between linearly independent solutions of the Schrödinger equation provide a rigorous basis for some of the assumptions of the SEM-CFM, like, for example, the concept of "saturation". We compare the performance of both approaches on a simple one-dimensional model and suggest that taking into account the asymptotic behaviour of the wavefunction (as is already done in the WM) may make the SEM-CFM more efficient from a numerical point of view.

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  • We compare the Wronskian method (WM) and the Schrödinger eigenvalue march or canonical function method (SEM--CFM) for the calculation of the energies and eigenfunctions of the...

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