Exact solutions for the inverse problem of the time-independent Schrödinger equation

2024/11/21 by Bhavika Bhalgamiya, M. A. Novotny · 1 voice
Physics and Astronomy · #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems

paper · pdf · doi:10.1119/5.0172824

openalex publication_date 2024/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26

Abstract

We introduce an “inverse method” for solving the time-independent Schrödinger equation. Rather than derive wave functions that are solutions for a given external potential V(r→), we ask the inverse question of which V(r→) will have a given probability density function P(r→). Several examples of ground states in one, two, and three dimensions are presented for both well-known and more exotic probability density functions in position space.

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• doi.org/10.1119/5.01... #PhysicsEducation #PhysicsTeachers #PhysicsResearch #AJP [bsky, 4 points, 0 comments]

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