The Effective β Value in a Simple Harmonic Oscillator Wave Function

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 (\, \beta_\rm effective). We obtain the analytical expression of \, \beta_\rm eff(\, \beta_\rm effective) of the SHO wave function in coordinate space and momentum space. The expression is applied to the light meson system (u\baru, ~u\bars) to compare the behavior of \, \beta_\rm eff. The results show that \, \beta_ \rm eff, \, \boldsymbolr in coordinate space and \, \beta_ \rm eff, \, \boldsymbolp in momentum space are significantly different in the ground state, however, similar in the highly excited states with Cornell potential.