In quantum mechanics, the energy of a hydrogen atom is minimized when the principal quantum number n is 1. However, the author has previously pointed out that the hydrogen atom has a state where n=0. An electron in th...In quantum mechanics, the energy of a hydrogen atom is minimized when the principal quantum number n is 1. However, the author has previously pointed out that the hydrogen atom has a state where n=0. An electron in the state where n=0has zero rest mass energy. However, a hydrogen atom has an energy level even lower than the n=0state. This is hard to accept from the standpoint of common sense. Thus, the author has previously pointed out that an electron at the energy level where n=0has zero energy because the positive energy mec2and negative energy −mec2cancel each other out. This paper elucidates the strange relationship between the momentum of a photon emitted when a hydrogen atom is formed by an electron with such characteristics, and the momentum acquired by the electron.展开更多
In this paper, we present a structure for obtaining the exact eigenfunctions and eigenvalues of the Jaynes-Cummings model （JCM） without the rotating wave approximation （RWA）. We study the evolution of the system i...In this paper, we present a structure for obtaining the exact eigenfunctions and eigenvalues of the Jaynes-Cummings model （JCM） without the rotating wave approximation （RWA）. We study the evolution of the system in the strong coupling region using the time evolution operator without RWA. The entanglement of the system without RWA is investigated using the Von Neumann entropy as an entanglement measure. It is interesting that in the weak coupling regime, the population of the atomic levels and Von Neumann entropy without RWA model shows a good agreement with the RWA whereas in strong coupling domain, the results of these two models are quite different.展开更多
文摘In quantum mechanics, the energy of a hydrogen atom is minimized when the principal quantum number n is 1. However, the author has previously pointed out that the hydrogen atom has a state where n=0. An electron in the state where n=0has zero rest mass energy. However, a hydrogen atom has an energy level even lower than the n=0state. This is hard to accept from the standpoint of common sense. Thus, the author has previously pointed out that an electron at the energy level where n=0has zero energy because the positive energy mec2and negative energy −mec2cancel each other out. This paper elucidates the strange relationship between the momentum of a photon emitted when a hydrogen atom is formed by an electron with such characteristics, and the momentum acquired by the electron.
文摘In this paper, we present a structure for obtaining the exact eigenfunctions and eigenvalues of the Jaynes-Cummings model （JCM） without the rotating wave approximation （RWA）. We study the evolution of the system in the strong coupling region using the time evolution operator without RWA. The entanglement of the system without RWA is investigated using the Von Neumann entropy as an entanglement measure. It is interesting that in the weak coupling regime, the population of the atomic levels and Von Neumann entropy without RWA model shows a good agreement with the RWA whereas in strong coupling domain, the results of these two models are quite different.
