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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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How to see the ${\rm SO}(4)$ symmetry of the classical Kepler problem?
It is well-known that the hidden symmetry of the $1/r$-problem $$H=\frac{{\bf p}^2}{2m}-\frac{k}{r}\tag{1}$$ is ${\rm SO(4)}$ in the sense that the components of angular momentum $L_i$ and those of th …
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