单个谐振子波函数中的有效<b><i>β</i></b>值

单个谐振子波函数中的有效β值

摘要: 当一个简单谐振子波函数(SHO)作为有效波函数时，在SHO波函数里面一个重要的参数是有效 \, \beta值。得到了简单谐振子波函数有效 \, \beta值( \, \beta_\rm eff)在坐标空间和动量空间的解析表达式。将解析式运用到轻介子系统(u\baru, \, u\bars)比较 \, \beta_\rm eff的行为，结果表明在基态时坐标空间的 \, \beta_ \rm eff, \, \boldsymbolr和动量空间的 \, \beta_ \rm eff, \, \boldsymbolp在康奈尔势下的值不相同，而在高激发态时两者大小相近。

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 \, \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.