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从体系计算中讨论海森伯不确定关系

A discussion on Heisenberg’s uncertainty relation based on the calculation of some typical systems

  • 摘要: 文章作者对量子力学与经典力学中的几个典型体系进行了计算,求出了粒子位置与动量的不确定量x2-x2和p2-p2.计算结果表明,不同状态下的不确定量之积是不一样的.谐振子和无限深势阱的实例计算还说明,与量子力学不确定关系相类似的关系在经典力学中也存在.它使人们对海森伯不确定关系有了新的认识,并对量子力学的波函数有了更深刻的了解.文章最后讨论了两个相关的实验现象.

     

    Abstract: We calculate the uncertain quantities of particle position and momentum, x2-x2 and p2-p2, using a few typical systems from classical and quantum mechanics. The results show that the product of the uncertain quantities varies with different states. Taking the harmonic oscillator and infinitely deep potential well as examples, we show that a relation analogous to the uncertainty relation of quantum mechanics also exists in classical mechanics. This gives a new understanding of the Heisenberg uncertainty relation, and provides additional insight into the wave function of quantum mechanics. Finally, two related experimental phenomena are discussed.

     

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