Abstract: Applications of Laplace- Runge-Lenz vector in classical mechanics, quantum mechanics and general relativity are reviewed briefly. By using this vector conserved in classical and quantum Kepler problems, one can study some important properties, such as obit equation and eigenvalue of energy, without solving the equa- tions of motion. Although the corrections from general relativity violate the conservation, its evolution, with respect to time, will completely determine the perihelion precession and light bending. All these examples indicate that La- place-Runge-Lenz vector is a fundamental physics quantity which is dictated by basic dynamical symmetries, thus it is instructive to introduce it into general physics courses.

Key words: Laplace- Runge- Lenz vector, Kepler problem, perihelion precession, light bending, hydrogenenergy levels