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WKB approximation under a Killingbeck potential and its application to double-heavy-meson spectroscopy

Cheng-Qun Pang1,*, Lhamo Chosto2,3, Ya-Rong Wang4, Zhi-Bin Gao5, Hao Chen3,6,†, Yu-Long Kang3,6,7,‡, and Wei Li3

  • 1School of Physics and Optoelectronic Engineering, Ludong University, Yantai 264000, China
  • 2Gonghe County Senior High School, Qinghai Province, Gonghe 811800, China
  • 3College of Physics and Electronic Information Engineering, Qinghai Normal University, Xining 810000, China
  • 4Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin 300350, China
  • 5School of General Education, Qinghai Polytechnic University, Xining 810000, China
  • 6Academy of Plateau Science and Sustainability, Xining 810016, China
  • 7Qinghai Key Laboratory of Advanced Technology and Application of Environmental Functional Materials, Xining 810016, China

  • *Contact author: xuehua45@163.com
  • †Contact author: chenhao_qhnu@outlook.com
  • ‡Contact author: kungyulong@163.com
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Phys. Rev. C 114, 045205 – Published 13 October, 2026

DOI: https://doi.org/10.1103/kl6h-yyb6

Abstract

It is well known that nonrelativistic or semirelativistic constituent quark models can describe a large number of the meson and baryon properties with surprising accuracy. In this work, we study the Killingbeck potential using the WKB approximation in the constituent quark model. The implicit approximate solutions for the energy eigenvalues, together with analytical expressions for the root-mean-square radii and the probability densities at the origin, of the Schrödinger equation are obtained by using appropriate quantization conditions. Finally, we discuss applications to double-heavy-meson spectroscopy within the Killingbeck potential.

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Phys. Rev. C 114, 045205– Published 13 October, 2026
  • Received 3 June 2025
  • Revised 7 July 2026
  • Accepted 10 September 2026
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