量子力学中的位置或动量都不能精确测量
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摘要
对量子力学测量公设和不确定性原理的一个普遍的误解是,如果单独测量位置或者动量,可以精确测量.本文以在谐振子基态上测量位置为例,说明精确测量位置需要无限大的能量.因此,量子力学中的位置或者动量都不能精确测量.
A misconception in quantum mechanics is that when the measurement of position or momentum alone is performed, completely accurate values will be obtained. We take the measurement of position for an oscillator in a ground state for instance, and calculations show that the oscillator must gain some energy during the measurement and the amount of the energy increases without bound along with degree of the accuracy. Therefore, neither position nor momentum can be accurately measured.
A misconception in quantum mechanics is that when the measurement of position or momentum alone is performed, completely accurate values will be obtained. We take the measurement of position for an oscillator in a ground state for instance, and calculations show that the oscillator must gain some energy during the measurement and the amount of the energy increases without bound along with degree of the accuracy. Therefore, neither position nor momentum can be accurately measured.
引文
[1] C. Cohen-Tannoudji, Diu b, Laloe F. Quantum Mechanics I [M]: Paris: Hermann, 1977:220.
[2] 王竹溪,郭敦仁. 特殊函数概论[M].北京:科学出版社,1979:361.
[3] Liu Q H, Kuang S Q, Li Z,et al. Finite energy transfer and better approximations of delta function in the position measurement [EB/OL]. arXiv:1808.05165,2018.8.
[2] 王竹溪,郭敦仁. 特殊函数概论[M].北京:科学出版社,1979:361.
[3] Liu Q H, Kuang S Q, Li Z,et al. Finite energy transfer and better approximations of delta function in the position measurement [EB/OL]. arXiv:1808.05165,2018.8.