The classical limit of the quantum mechanical Kepler problem is derived by using a simple mathematical procedure recently proposed. The method is based both on Bohr’s correspondence principle and the local averages o...The classical limit of the quantum mechanical Kepler problem is derived by using a simple mathematical procedure recently proposed. The method is based both on Bohr’s correspondence principle and the local averages of the quantum probability distribution. We illustrate in a clear fashion the difference between Planck’s limit and Bohr’s correspondence principle. We discuss the confinement effect in macroscopic systems.展开更多
Beginning with a Lagrangian, we derived an approximate relativistic orbit equation which describes relativistic corrections to Keplerian orbits. The critical angular moment to guarantee the existence of periodic orbit...Beginning with a Lagrangian, we derived an approximate relativistic orbit equation which describes relativistic corrections to Keplerian orbits. The critical angular moment to guarantee the existence of periodic orbits is determined. An approximate relativistic Kepler’s elliptic orbit is illustrated by numerical simulation via a second-order perturbation method of averaging.展开更多
The generalized Lagrangian is defined in a dissipative electromagnetic medium on the basis of the combination of dynamical analysis and fractional derivative. Lorentz medium models are obtained by formulating relevant...The generalized Lagrangian is defined in a dissipative electromagnetic medium on the basis of the combination of dynamical analysis and fractional derivative. Lorentz medium models are obtained by formulating relevant Euler-Lagrange equations. The invariance is obtained subsequently by investigating the invariance of time variation in the system, and then the relation between the related Hamiltonian and electromagnetic energy density is investigated. Canonical equations are obtained eventually. The electrodynamic interpretation on dissipative electromagnetic systems is revealed.展开更多
In the first part of this paper, we found a more convenient algorithm for solving the equation of motion of a system of n bodies. This algorithm consists in solving first the trajectory equation and then the temporal ...In the first part of this paper, we found a more convenient algorithm for solving the equation of motion of a system of n bodies. This algorithm consists in solving first the trajectory equation and then the temporal equation. In this occasion, we will introduce a new way to solve the temporal equation by curving the horizontal axis (the time axis). In this way, we will be able to see the period of some periodic systems as the length of a certain curve and this will allow us to approximate the period in a different way. We will also be able to solve some problems like the pendulum one without using elliptic integrals. Finally, we will solve Kepler’s problem using all the formalism.展开更多
文摘The classical limit of the quantum mechanical Kepler problem is derived by using a simple mathematical procedure recently proposed. The method is based both on Bohr’s correspondence principle and the local averages of the quantum probability distribution. We illustrate in a clear fashion the difference between Planck’s limit and Bohr’s correspondence principle. We discuss the confinement effect in macroscopic systems.
文摘Beginning with a Lagrangian, we derived an approximate relativistic orbit equation which describes relativistic corrections to Keplerian orbits. The critical angular moment to guarantee the existence of periodic orbits is determined. An approximate relativistic Kepler’s elliptic orbit is illustrated by numerical simulation via a second-order perturbation method of averaging.
基金Supported by the National Natural Science Foundation of China under Grant Nos 60601028.
文摘The generalized Lagrangian is defined in a dissipative electromagnetic medium on the basis of the combination of dynamical analysis and fractional derivative. Lorentz medium models are obtained by formulating relevant Euler-Lagrange equations. The invariance is obtained subsequently by investigating the invariance of time variation in the system, and then the relation between the related Hamiltonian and electromagnetic energy density is investigated. Canonical equations are obtained eventually. The electrodynamic interpretation on dissipative electromagnetic systems is revealed.
文摘In the first part of this paper, we found a more convenient algorithm for solving the equation of motion of a system of n bodies. This algorithm consists in solving first the trajectory equation and then the temporal equation. In this occasion, we will introduce a new way to solve the temporal equation by curving the horizontal axis (the time axis). In this way, we will be able to see the period of some periodic systems as the length of a certain curve and this will allow us to approximate the period in a different way. We will also be able to solve some problems like the pendulum one without using elliptic integrals. Finally, we will solve Kepler’s problem using all the formalism.
