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arXiv · 2112.03672

The effective $β$ value in a Simple Harmonic Oscillator wave function

Chao-hui Wang·Long Tang·Ting-yan Li·Gong-ping Zheng·Jing-fu Hu·Cheng-qun Pang
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Abstract

When a Simple Harmonic Oscillator (SHO) wave function is used as an effective wave function, a very important parameter in the SHO wave function is the effective $β$ value. We obtain the analytical expression of $β_{eff}$ ($β_{effective}$) of the SHO wave function in coordinate space and momentum space. The expression is applied to the light meson system $(u\bar{u},~u\bar{s})$ to compare the behavior of $β_{eff}$. The results show that $β_ {eff,\mathbf{r}}$ in coordinate space and $β_ {eff,\mathbf{p}}$ in momentum space are significantly different in the ground state, however, similar in the highly excited states with Cornell potential.

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Chao-hui Wang, Long Tang, Ting-yan Li, Gong-ping Zheng, Jing-fu Hu, Cheng-qun Pang. 2022-07-13. The effective $β$ value in a Simple Harmonic Oscillator wave function. https://doi.org/10.11804/nuclphysrev.39.2022012

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