【作者】 周宙安；

【导师】 廖树帜；

【作者基本信息】 湖南师范大学 ， 理论物理， 2006， 硕士

【摘要】 首先介绍了位置与动量的广义测不准关系，由此得到了位置的最小不确定度，与此相应的微观状态的态密度必须作出修正，该修正对我们当前前沿科学所遇到的许多问题将产生广泛的影响。例如对黑体辐射问题，我们的讨论显示，与Planck温度比较在温度比较高的情况下斯特藩一玻耳兹曼定律并不成立，辐射场的总能量应该与温度成正比。其次，将广义测不准关系的应用拓展到黑洞熵的计算，利用经广义测不准关系改进的薄层brick-wall方法计算了黑洞熵。结果表明，由这种方法得到的黑洞熵上限与它的外视界和宇宙视界面积之和成正比，和人们预期的结果相符，从中揭示了黑洞熵与视界面积之间的内在联系，也进一步表明了黑洞熵是视界面上量子态的熵，是一种量子效应。广义测不准关系的引入使我们看到，brick-wall方法与引力场量子化可能存在着一些内在的联系。最后，利用量子力学的能量与时间的测不准关系，计算了光频的引力红移，结果表明，由这种方法得到的引力红移量与人们预期的结果相符。更多还原

【Abstract】 First of all, the generalized position-momentum uncertainty relation,which leads to a finite minimum uncertainty of position, is introduced.Accordingly, the density of quantum states needs to be modified. This isbelieved to have a very broad effect on our current knowledge of variousproblems. In the specific example of the blackbody radiation, we havefound that the Stephan-Boltzmann law needs to be modified at very hightemperatures compared with the Planck temperature, i.e., the energy of theradiation field as a whole will be proportional to the temperature.Second, the generalized uncertainty relation is applied to thecalculation of the entropy as well. The entropy is calculated by theimproved brick-wall method due to the generalized uncertainty relation.The entropy bound of this system not only includes the contribution of theblack hole horizon, but also includes the contribution of the cosmologicalhorizon, which is consistent with what people anticipate. It is found thatthere is an internal relation between the event horizon and the entropy; itis further revealed that the black hole entropy is an entropy which belongsto event horizon and is a kind of quantum effect. It is also apparent thatthe cut-off in brick-wall model is something related to the quantum theoryof gravity.Last but not least, we also calculate the red-shift of light frequency for gravitation by using the energy-time of the uncertainty relation ofquantum mechanical, It is shown that the result of the red-shift of lightfrequency for gravitation obtained by this method accords with the oneexpected by some people.更多还原