Improved power-series method for confined one-dimensional quantum-mechanical problems

2016/02/23 by Francisco M. Fernández, Fernández, Francisco M.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Fractional Differential Equations Solutions #Model Reduction and Neural Networks #Numerical methods for differential equations #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.1602.07299

arxiv created 2016/02/23 · openalex publication_date 2016/02/23 · arxiv updated 2016/02/25 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We propose two improvements to the well-known power series method for confined one-dimensional quantum-mechanical problems. They consist of the addition of a variational step were the energy plays the role of a variational parameter. We compare the rate of convergence of the three methods on an exactly-solvable model. We also outline possible generalizations of the approaches to more complex problems.

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