The Average Uncertainty of a Three Dimensional Nuclear Oscillator

Consider a three dimensional nuclear oscillator in a solid. The position vector is r = ((A cos a))$^2$ +(B cos b)$^2$ +(C cos c)$^2$)$^{1/2}$, where A,B,C are amplitudes of oscillation. If A=B=C, $\Delta$ p $\geq$ h/2($\pi$)($\Delta$ r), p(av)is the average momentum of the oscillator, a=b=c, then $\Delta$ p(av)= h/2($\pi$)(3$\Delta$A cos$^2$)$^{1/2}$, if $\Delta$ A is the uncertainty in the amplitude. The maximum cos = 1, minimum cos = 0 and RMS cos =0.707(average) so max.uncertainty $\Delta$ p(av)= infinite, min uncertainty $\Delta$ p(av)$\geq$ h/10.83$\Delta$ A and average uncertainty $\Delta$ p (av)=h/3.45 $\Delta$A. This paper suggests the concept of average uncertainty.