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

Laplace–Runge–Lenz Vector - Context

... E and the three Cartesian components of the angular momentum

... 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

... 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

... 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

... 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 ...Main Site Subjects

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