Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Rational Extension of Anisotropic Harmonic Oscillator Potentials in Higher Dimensions

Rajesh Kumar, Rajesh Kumar Yadav, Avinash Khare

Abstract

This paper presents the first-order supersymmetric rational extension of the quantum anisotropic harmonic oscillator (QAHO) in multiple dimensions, including full-line, half-line, and their combinations. The exact solutions are in terms of the exceptional orthogonal polynomials. The rationally extended potentials are isospectral to the conventional QAHOs.

Rational Extension of Anisotropic Harmonic Oscillator Potentials in Higher Dimensions

Abstract

This paper presents the first-order supersymmetric rational extension of the quantum anisotropic harmonic oscillator (QAHO) in multiple dimensions, including full-line, half-line, and their combinations. The exact solutions are in terms of the exceptional orthogonal polynomials. The rationally extended potentials are isospectral to the conventional QAHOs.

Paper Structure

This paper contains 10 sections, 83 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. One-Dimensional Harmonic Oscillator
  3. Half-Line Oscillator
  4. Two-Dimensional Anisotropic Harmonic Oscillator
  5. $2$D-Full-line oscillator
  6. 2D-Half-Line Oscillator
  7. One Full-Line and One Half-Line Oscillator
  8. Three-Dimensional Anharmonic Harmonic Oscillator
  9. Full-Line Oscillator with two equal frequencies
  10. Conclusions and Open Problem

Figures (1)

  • Figure 1: Eigenfunctions for RE Half-Line oscillator.