journal article·2023-11-01Open access

WKB solutions of the Schrödinger equation with a quartic potential

C. Z. Xiao, Q. Wang, J. F. Myatt

AIP Advances· Volume 13· Issue 11

Abstract

The Schrödinger equation with a quartic potential is a fundamental equation describing the physics of stimulated side scattering, but no exact, even approximate solution has been formulated yet. Here, the approximate solutions to such a Schrödinger equation are derived using the WKBJ method under different variables. The solutions are accurate enough in most cases. Eigenvalues and eigenfunctions, which are the most impressive properties of such equations, are also discussed.
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Research context

OpenAlex topics: Laser-Plasma Interactions and Diagnostics · High-pressure geophysics and materials · Terahertz technology and applications

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Affiliations

School of Physics and Electronics, Hunan University 1 , Changsha 410082, China

Department of Electrical and Computer Engineering, University of Alberta 2 , 9211 116, St. NW, Edmonton, Alberta T6G 1H9, Canada

Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University 3 , Shanghai 200240, China

Institute of Applied Physics and Computational Mathematics 4 , Beijing 100094, China

Funding

Strategic Priority Research Program of Chinese Academy of Sciences · National Natural Science Foundation of China · National Science Foundation of Hunan Province · China Postdoctoral Science Foundation · Natural Sciences and Engineering Research Council of Canada

References (14)

Show source-provided references
1. Phys. Rev. E · 2023 · 107 · 02520310.1103/physreve.107.025203 ↗
2. Phys. Plasmas · 2023 · 30 · 07270210.1063/5.0152261 ↗
3. Phys. Fluids · 1974 · 17 · 121110.1063/1.1694867 ↗
4. Phys. Fluids · 1985 · 28 · 339710.1063/1.865340 ↗
5. Phys. Plasmas · 2020 · 27 · 04270310.1063/1.5131158 ↗
6. Phys. Rev. E · 2021 · 104 · 06520310.1103/physreve.104.065203 ↗
7. Phys. Rev. Lett. · 1979 · 42 · 64410.1103/physrevlett.42.644 ↗
8. Phys. Rev. E · 2019 · 99 · 03320310.1103/physreve.99.033203 ↗
9. Plasma Phys. Controlled Fusion · 2018 · 60 · 02502010.1088/1361-6587/aa9b41 ↗
10. 2010
11. 1962
12. Trans. Camb. Philos. Soc. · 1847 · 9 · 379
13. 2010
14. Phys. Rev. Lett. · 1972 · 29 · 56510.1103/physrevlett.29.565 ↗