不确定原理和自由粒子的量子理论

UNCERTAINTY PRINCIPLE AND QUANTUM THEORY OF FREE PARTICLE

根据不确定原理和“不同惯性系测得的同一事件的概率是相同的”的原则直接得到了非相对论性的和相对论性的点粒子在位置完全确定时的速度和动量的概率分布密度函数以及自由粒子的位置分布密度和三维流密度函数．另外，给出了Ｄｉｒａｃ理论框架内的三个积分公式，在此基础上提出了对处于状态｜ψ＞的系统进行力学量Ａ的测量时测得结果为αｎ的概率的新的计算规则．

In this paper,based on the uncertainty principle and the principle of 'the probability of an event measured by different inertial framrs is same', we obtain directly the probability distribution density function of velocity and momentum of non-relativistic and relativistic point particle when the position of the particle is fully measured, and obtain directly the position distribution function and threedimensional current density of a tree particle. Among these conclusions, the conclusions in relativistic case are different from current quantum mechanics.Besides, we obtain three integration formulas in Dirac theory,and according to these formulas give new calculative rule of the probability that the eigen-value αn is observed when physical quantity A is measured for a state described by the state vector |ψ>.