ScholarLens Back to search
1999•Journal of Physics A Mathematical and GeneralOpen access

The accuracy of semiclassical quantization for an integrable system - the hyperspherical billiard

Saar Rahav, Oded Agam, Shmuel Fishman

Open full text 5 citations

Abstract

The eigenvalues of the hyperspherical billiard are calculated in the semiclassical approximation. The eigenvalues where this approximation fails are identified and found to be related to caustics that approach the wall of the billiard. The fraction of energy levels for which the semiclassical error is larger than some given value is calculated analytically (and tested numerically) and found to be independent of energy. The implications for other systems, in particular integrable ones, are discussed.

Open-access reader

About this research paper

What this paper is about

The eigenvalues of the hyperspherical billiard are calculated in the semiclassical approximation. The eigenvalues where this approximation fails are identified and found to be related to caustics that approach the wall of the billiard. The fraction of energy levels for which the semiclassical error is larger than some given value is calculated analytically (and tested numerically) and found to be independent of energy. The implications for other systems, in particular integrable ones, are discussed.

Why it matters

OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

The eigenvalues of the hyperspherical billiard are calculated in the semiclassical approximation. The eigenvalues where this approximation fails are identified and found to be related to caustics that approach the wall of the billiard. The fraction of energy levels for which the semiclassical error is larger than some given value is calculated analytically (and tested numerically) and found to be independent of energy. The implications for other systems, in particular integrable ones, are discussed.

Key concepts: Semiclassical physics, Dynamical billiards, Integrable system, Eigenvalues and eigenvectors, Quantization (signal processing), Physics, Mathematical physics, Quantum mechanics

Related papers

Related paper 1Related paper 2
Back to paper searchBrowse research topicsOriginal source
The accuracy of semiclassical quantization for an integrable system - the hyperspherical billiard — Research Paper | ScholarLens