Uniform Asymptotic Approximation Method with Pöschl–Teller Potential-Reference-Cited by-同舟云学术

Uniform Asymptotic Approximation Method with Pöschl–Teller Potential

Published:2023-10-31 Issue:11 Volume:9 Page:471
ISSN:2218-1997
Container-title:Universe
language:en
Short-container-title:Universe

Author:

Pan Rui¹^ORCID,Marchetta John Joseph²,Saeed Jamal¹^ORCID,Cleaver Gerald²^ORCID,Li Bao-Fei³⁴,Wang Anzhong¹^ORCID,Zhu Tao³⁴^ORCID

Affiliation:

1. GCAP-CASPER, Physics Department, Baylor University, Waco, TX 76798-7316, USA

2. EUCOS-CASPER, Physics Department, Baylor University, Waco, TX 76798-7316, USA

3. Institute for Advanced Physics & Mathematics, Zhejiang University of Technology, Hangzhou 310032, China

4. United Center for Gravitational Wave Physics (UCGWP), Zhejiang University of Technology, Hangzhou 310032, China

Abstract

In this paper, we study analytical approximate solutions for second-order homogeneous differential equations with the existence of only two turning points (but without poles) by using the uniform asymptotic approximation (UAA) method. To be more concrete, we consider the Pöschl–Teller (PT) potential, for which analytical solutions are known. Depending on the values of the parameters involved in the PT potential, we find that the upper bounds of the errors of the approximate solutions in general are ≲0.15∼10% for the first-order approximation of the UAA method. The approximations can be easily extended to high orders, for which the errors are expected to be much smaller. Such obtained analytical solutions can be used to study cosmological perturbations in the framework of quantum cosmology as well as quasi-normal modes of black holes.

Funder

the US Natural Science Foundation

the Baylor Physics graduate program

the National Key Research and Development Program of China

the National Natural Science Foundation of China

the Zhejiang Provincial Natural Science Foundation of China

the Fundamental Research Funds for the Provincial Universities of Zhejiang in China

Publisher

MDPI AG

Subject

General Physics and Astronomy

Link

https://www.mdpi.com/2218-1997/9/11/471/pdf

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