The discovery of the Planck relation is generally regarded as the starting point of quantum physics.Planck＇s constant h is now regarded as one of the most important universal constants.The physical nature of h,howeve...The discovery of the Planck relation is generally regarded as the starting point of quantum physics.Planck＇s constant h is now regarded as one of the most important universal constants.The physical nature of h,however,has not been well understood.It was originally suggested as a fitting constant to explain the black-body radiation.Although Planck had proposed a theoretical justification of h,he was never satisfied with that.To solve this outstanding problem,we use the Maxwell theory to directly calculate the energy and momentum of a radiation wave packet.We find that the energy of the wave packet is indeed proportional to its oscillation frequency.This allows us to derive the value of Planck＇s constant.Furthermore,we show that the emission and transmission of a photon follows the all-or-none principle.The ＂strength＂ of the wave packet can be characterized by ζ,which represents the integrated strength of the vector potential along a transverse axis.We reason that ζ should have a fixed cut-off value for all photons.Our results suggest that a wave packet can behave like a particle.This offers a simple explanation to the recent satellite observations that the cosmic microwave background follows closely the black-body radiation as predicted by Planck＇s law.展开更多
Bose-Einstein condensation is a state of matter known to be responsible for peculiar properties exhibited by superfluid Helium-4 and superconductors. Bose-Einstein condensate （BEC） in its pure form is realizable wit...Bose-Einstein condensation is a state of matter known to be responsible for peculiar properties exhibited by superfluid Helium-4 and superconductors. Bose-Einstein condensate （BEC） in its pure form is realizable with alkali atoms under ultra-cold temperatures. In this paper, we review the experimental scheme that demonstrates the atomic Bose-Einstein condensate. We also elaborate on the theoretical framework for atomic Bose-Einstein condensation, which includes statistical mechan- ics and the Gross-Pitaevskii equation. As an extension, we discuss Bose-Einstein condensation of photons realized in a fluorescent dye filled optical microcavity. We analyze this phenomenon based on the generalized Planck＇s law in statistical mechanics. Further, a comparison is made between photon condensateand laser. We describe how photon condensate may be a possible alternative for lasers since it does not require an energy consuming population inversion process.展开更多
基金Project partially supported by the Research Grant Council of Hong Kong,China(Grant No.RGC 660207)the Macro-Science Program,Hong Kong University of Science and Technology,China(Grant No.DCC 00/01.SC01)
文摘The discovery of the Planck relation is generally regarded as the starting point of quantum physics.Planck＇s constant h is now regarded as one of the most important universal constants.The physical nature of h,however,has not been well understood.It was originally suggested as a fitting constant to explain the black-body radiation.Although Planck had proposed a theoretical justification of h,he was never satisfied with that.To solve this outstanding problem,we use the Maxwell theory to directly calculate the energy and momentum of a radiation wave packet.We find that the energy of the wave packet is indeed proportional to its oscillation frequency.This allows us to derive the value of Planck＇s constant.Furthermore,we show that the emission and transmission of a photon follows the all-or-none principle.The ＂strength＂ of the wave packet can be characterized by ζ,which represents the integrated strength of the vector potential along a transverse axis.We reason that ζ should have a fixed cut-off value for all photons.Our results suggest that a wave packet can behave like a particle.This offers a simple explanation to the recent satellite observations that the cosmic microwave background follows closely the black-body radiation as predicted by Planck＇s law.
文摘Bose-Einstein condensation is a state of matter known to be responsible for peculiar properties exhibited by superfluid Helium-4 and superconductors. Bose-Einstein condensate （BEC） in its pure form is realizable with alkali atoms under ultra-cold temperatures. In this paper, we review the experimental scheme that demonstrates the atomic Bose-Einstein condensate. We also elaborate on the theoretical framework for atomic Bose-Einstein condensation, which includes statistical mechan- ics and the Gross-Pitaevskii equation. As an extension, we discuss Bose-Einstein condensation of photons realized in a fluorescent dye filled optical microcavity. We analyze this phenomenon based on the generalized Planck＇s law in statistical mechanics. Further, a comparison is made between photon condensateand laser. We describe how photon condensate may be a possible alternative for lasers since it does not require an energy consuming population inversion process.
