We study the uncertainty relation for three quantum systems in the N-dimensional space by using the virial theorem (VT). It is shown that this relation depends on the energy spectrum of the system as well as on the sp...We study the uncertainty relation for three quantum systems in the N-dimensional space by using the virial theorem (VT). It is shown that this relation depends on the energy spectrum of the system as well as on the space dimension N. It is pointed out that the form of lower bound of the inequality, which is governed by the ground state, depends on the system and on the space dimension N. A comparison between our result for the lower bound and recent results, based on information-theoretic approach, is pointed out. We examine and analyze these derived uncertainties for different angular momenta with a special attention made for the large N limit.展开更多
Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the f...Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the first attempt at calculating the energy spectrum for this potential, which was introduced by H. Bahlouli and A. D. Alhaidari and for which they obtained the “potential parameter spectrum”. Our results are also independently verified using a direct method of diagonalizing the Hamiltonian matrix in the J-matrix basis.展开更多
In the hydrogen molecular ion, the kinetic energy lowering of the electron is associated with its delocalization due to electron exchange between the two protons of the molecule. This decrease in the kinetic energy of...In the hydrogen molecular ion, the kinetic energy lowering of the electron is associated with its delocalization due to electron exchange between the two protons of the molecule. This decrease in the kinetic energy of the exchanged electron in the hydrogen molecular ion and the decrease in the dynamical mass of the two exchanged pions in the nucleon-nucleon interaction are at the origin of the attraction mechanism in the molecular covalent bonding and in the nuclear interaction. Based on this unitary approach of the attraction mechanism, the formulas of molecular potential and central nucleon-nucleon potential were derived. The decrease in the mass of the exchanged pions in the nucleon-nucleon bound state, actually means the decrease in the mass of the nucleons. This nucleon mass decrease could be a manifestation of the partial chiral symmetry restoration in nuclear matter.展开更多
文摘We study the uncertainty relation for three quantum systems in the N-dimensional space by using the virial theorem (VT). It is shown that this relation depends on the energy spectrum of the system as well as on the space dimension N. It is pointed out that the form of lower bound of the inequality, which is governed by the ground state, depends on the system and on the space dimension N. A comparison between our result for the lower bound and recent results, based on information-theoretic approach, is pointed out. We examine and analyze these derived uncertainties for different angular momenta with a special attention made for the large N limit.
文摘Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the first attempt at calculating the energy spectrum for this potential, which was introduced by H. Bahlouli and A. D. Alhaidari and for which they obtained the “potential parameter spectrum”. Our results are also independently verified using a direct method of diagonalizing the Hamiltonian matrix in the J-matrix basis.
文摘In the hydrogen molecular ion, the kinetic energy lowering of the electron is associated with its delocalization due to electron exchange between the two protons of the molecule. This decrease in the kinetic energy of the exchanged electron in the hydrogen molecular ion and the decrease in the dynamical mass of the two exchanged pions in the nucleon-nucleon interaction are at the origin of the attraction mechanism in the molecular covalent bonding and in the nuclear interaction. Based on this unitary approach of the attraction mechanism, the formulas of molecular potential and central nucleon-nucleon potential were derived. The decrease in the mass of the exchanged pions in the nucleon-nucleon bound state, actually means the decrease in the mass of the nucleons. This nucleon mass decrease could be a manifestation of the partial chiral symmetry restoration in nuclear matter.
