Year: 1999
Type: article
Abstract: We define Sturmian basis functions for the harmonic oscillator, and investigate whether recent insights into Sturmians for Coulomb-like potentials can be extended to this important potential. We also treat many-body problems such as coupling to a bath of harmonic oscillators. Comments on coupled oscillators and time-dependent potentials are also made. It is argued that the Sturmian method amounts to a nonperturbative calculation of the energy levels, but the limitations of the method is also pointed out, and the cause of this limitation is found to be related to the divergence of the potential. Thus the divergent nature of the anharmonic potential leads to the Sturmian method being less accurate than in the Coulomb case. We discuss how modified anharmonic oscillator potentials, which are well behaved at infinity, leads to a rapidly converging Sturmian approximation.
Source: Physical Review A
Author: Frank Antonsen
Institution: University of Copenhagen
Language: English
Topic: Atomic and Molecular Physics
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1992912202