无限深势阱中粒子动量概率分布的数值分析

Numerical analysis of momentum probability distribution of particle in infinite deep potential well

一维无限深势阱中本征态粒子的动量呈现负无穷到正无穷且有无数个节点的对称连续分布.本征态粒子的无量纲动量概率密度分布一般由两个主峰和无数的次峰组成,经典动量和最概然动量都分布在主峰区域内.数值计算结果表明动量谱在两个主峰区域内的概率极限值约为0.9028,测量所包含的次峰数量越多则粒子出现的概率越接近1.粒子经典动量分布是量子动量分布在高测量精度和大量子数条件下的极限.

The momentum of the eigenstate particle in the one-dimensional infinite deep potential well presents a symmetric and continuous distribution of negative infinity to positive infinity symmetry with countless nodes.The dimensionless momentum probability density distribution of the eigenstate particle is generally composed of two main peaks and numerous small peaks.Both the classical momentum and the most probable momentum are distributed in the region of the main peak.Numerical results show that the probability limit of momentum spectrum in two main peak regions is about 0.9028.The more the number of small peaks included in the measurement is,the closer the probability of the particle appearing is to 1.The classical momentum distribution of particle is the limit of the quantum momentum distribution under the condition of high measurement accuracy and large quantum number.