2015/10/13 by M. Reyes, Marco A. Reyes, Reyes, Marco A. +2 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1510.03735
13 pages, 5 figures. Accepted for publication in Revista Mexicana de Fisica
arxiv created 2015/10/13 · openalex publication_date 2015/10/13 · arxiv updated 2015/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Following a letter by Bassett, we show first that it is possible to find an analytical approximation to the error function in terms of a finite series of hyperbolic tangents from the supersymmetric (SUSY) solution of the Poschl-Teller eigenvalue problem in quantum mechanics (QM). Afterwards, we show that the second order differential equation for the derivatives of Dawson's function can be found in another SUSY related eigenvalue problem, where the factorization of the simple harmonic oscillator Hamiltonian renders the wrong-sign Hermite differential equation, and that Dawson's second order differential equation possess a singular SUSY type relation to this equation.