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 $\beta$ value. We obtain the analytical expression of $\beta_{ eff}$ ($\beta_{ effective}$) 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 $\beta_{ eff}$. The results show that $\beta_ { eff,\mathbf{ r}}$ in coordinate space and $\beta_ { eff,\mathbf{ p}}$ in momentum space are significantly different in the ground state, however, similar in the highly excited states with Cornell potential.
Categories: hep-ph quant-ph