Accurate eigenvalues of the Schrödinger equation with the potential V(r)=V₀r^α

2016/10/23 by Francisco M. Fernández, Fernández, Francisco M.
Engineering · Mathematics · Physics and Astronomy · #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Model Reduction and Neural Networks #Numerical methods for differential equations #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1610.07176

openalex publication_date 2016/10/23 · openalex created_date 2022/08/15 · openalex updated_date 2026/07/28

Abstract

We calculate accurate eigenvalues of the Schrödinger equation with the potential V(r)=V₀r^α, α≥ -1, V₀α>0. We resort to the Riccati-Padé method that is based on a rational approximation to the logarithmic derivative of the wavefunction. This approach applies when α is a rational number.

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