关键词: 对应原理, 统计分布, 不确定性关系

Abstract: Understanding the connection between quantum mechanics and classical physics is a crucial topic in physics. Bohr's hydrogen atom theory, particularly his concepts of stationary state quantization and the correspondence principle, provides a foundation for studying this connection. This paper applies Bohr's ideas to the onedimensional infinite square well model. By comparing the descriptions of the statistical distributions and uncertainties of particle position and momentum within the well given by classical statistical physics and quantum theory, we specifically examine a semiclassical approach. This approach derives the uncertainty relation using the quantized standing wave condition and classical statistical distribution, without solving the Schrdinger equation. Through a comparative analysis of the results derived from this method and the exact quantum mechanical solutions in the limit of large quantum numbers, we verify the validity of Bohr's correspondence principle within this model. Consequently, this work deepens our understanding of the transition mechanism by which quantum statistical behavior evolves into classical behavior．

Key words: correspondence principle, statistical distribution, uncertainty relation