单个谐振子波函数中的有效β值

The Effective β Value in a Simple Harmonic Oscillator Wave Function

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β值。得到了简单谐振子波函数有效β值(β_(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(uu,us)比较β_(eff)的行为,结果表明在基态时坐标空间的β_(eff,r)和动量空间的β_(eff,p)在康奈尔势下的值不相同,而在高激发态时两者大小相近。

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(β_(effective)).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 (uu,us) to compare the behavior of β_(eff).The results show that β_(eff,r) in coordinate space and β_(eff,p) in momentum space are significantly different in the ground state,however,similar in the highly excited states with Cornell potential.