# Lrl Vector

### Some articles on vector, lrl vector, vectors:

Laplace–Runge–Lenz Vector - Context
... E and the three Cartesian components of the angular momentum vector L ... by the particle's initial momentum p (or, equivalently, its velocity v) and the vector r between the particle and the center of force (see Figure 1, below) ... As defined below (see Mathematical definition), the Laplace–Runge–Lenz vector (LRL vector) A always lies in the plane of motion for any central force ...
Laplace–Runge–Lenz Vector - Conservation and Symmetry
... The conservation of the LRL vector corresponds to a subtle symmetry of the system ... conservation of both the angular momentum vector L and the LRL vector A (as defined above) and, quantum mechanically, ensures that the energy levels of hydrogen do not ... the higher symmetry group is SO(4), which preserves the length of four-dimensional vectors In 1935, Vladimir Fock showed that the quantum mechanical bound Kepler problem is equivalent to the problem of a free ...
Laplace–Runge–Lenz Vector
... In classical mechanics, the Laplace–Runge–Lenz vector (or simply the LRL vector) is a vector used chiefly to describe the shape and orientation of the orbit of ... More generally, the LRL vector is conserved in all problems in which two bodies interact by a central force that varies as the inverse square of the distance between them such problems are called Kepler problems ... The LRL vector was essential in the first quantum mechanical derivation of the spectrum of the hydrogen atom, before the development of the Schrödinger equation ...
Laplace–Runge–Lenz Vector - Alternative Scalings, Symbols and Formulations
... Unlike the momentum and angular momentum vectors p and L, there is no universally accepted definition of the Laplace–Runge–Lenz vector several different scaling factors and symbols are used in the ... to divide by the constant mk to obtain a dimensionless conserved eccentricity vector where v is the velocity vector ... This scaled vector e has the same direction as A and its magnitude equals the eccentricity of the orbit ...