Work

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

Year: 2024

Type: article

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.

Source: American Journal of Physics

DOI: 10.1119/5.0172824

Authors: Bhavika Bhalgamiya, Mark A. Novotny

Institution: Mississippi State University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: U.S. Department of Energy

Award: G731210326