On the functional form of the infinite square well model

2016/04/16 by Chyi-Lung Lin, Lin, Chyi-Lung
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1604.04680

openalex publication_date 2016/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The original model of the infinite square well contains a vague notation infinity and therefore results some ambiguities. We investigate to obtain a functional form for the potential energy V(x). This is done by substituting back the original energy eigenstates and eigenvalues into the Schrodinger equation. We then obtain a precise functional form of the V(x). From this reformed model, we show that energy eigenstates and eigenvalues can directly be obtained without the need of imposing boundary condition, Ehrenfest's theorem can directly be confirmed, and ambiguities in the original model can be resolved.

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