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Results tagged with laplace-runge-lenz-vector
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The Laplace–Runge–Lenz vector describes the shape and orientation of the orbit of one astronomical body around another. In general, the LRL vector is conserved (it's a constant of the motion) in all problems in which two bodies interact by a central force that varies as the inverse square of the distance between them (Kepler problem). Its conservation is significant in the quantization of the Hydrogen atom.
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Kepler problem: flows generated by constants of motion
The flow generated by a function $f$ on the phase space $T^*M$ (whose coordinate functions are $\mathbf{q}$ and $\mathbf{p}$) is a set of new coordinate functions $\mathbf{Q}(\mathbf{q}, \mathbf{p}, t …
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11
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$SO(4,2)$ symmetry of the hydrogen atom
$SO(4,2)$ is called the full dynamical group of the Kepler (or Hydrogen atom problem). The $SO(4)$ , $SO(3,2)$ and $SO(4,1)$ subgroups of $SO(4,2)$ are called partial dynamical groups.
Unlike symmet …
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