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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.
2
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Hydrogen atom as a free particle moving on a three dimensional sphere?
I have heard on various occasions that the Hamiltonian/Lagrangian of the Hydrogen atom or that of a particle moving in $1/r$-potential can be transformed into that of a free particle moving on the sur …
- 12.3k
-1
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answer
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Runge-Lenz vector when the earth is neither at the aphelion nor at the perihelion
Assuming the earth is either at the perihelion or at the aphelion, it is easy to see the Runge-Lenz (RL) vector is directed along the line joining the perihelion and aphelion. Since the RL vector is a …
- 12.3k
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answer
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Is this really $SO(4)$ algebra?
The commutation relations involving the components of Runge-Lenz vector of the Hydrogen atom problem, ${\vec A}$ and the angular momentum ${\vec L}$ are given by
$$
[L_i,L_j]=i\hslash\varepsilon_{ijk …
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