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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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Solving Hydrogen atom with ladder operators
The Hamiltonian of the hydrogen atom, $H=\mathbf{p}^2/2m - \alpha /|\mathbf{x}|$, commutes with all components of the angular momentum operator $\mathbf{L}= \mathbf{x} \times \mathbf{p}$ and of the La …
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