Abstract: 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.

Key words: dimensionless momentum probability density distribution function, probability, main peak, small peaks, accuracy of measurement