The runge-lenz-vector tag has no wiki summary.
3
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2answers
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Runge-Lenz vector and Keplerian Orbits
Is the loss of closed Keplerian orbits in relativistic mechanics directly tied to the absence of the Runge-Lenz vector?
2
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1answer
381 views
A Short way to show Conservation of Quantum Laplace–Runge–Lenz Vector?
I had been asked to prove the conservation of Quantum Laplace–Runge–Lenz Vector:
...
2
votes
1answer
99 views
Kepler problem: flows generated by constants of motion
This is part of an admission exam problem, found at
http://www.sissa.it/mp/admission/tests//2008_common.pdf
Consider the Hamiltonian of Kepler problem
$$H(\boldsymbol{r},\boldsymbol{p})= ...
1
vote
0answers
301 views
Square of Laplace–Runge–Lenz vector in Hydrogen atom [closed]
I have a problem. I've tried this question, but I don't get the correct expression. Can someone give me some ideas? Thanks!
Consider the Hydrogen Atom Hamiltonian:
$$
H = (\mathbf p^2/2 ...
3
votes
3answers
572 views
Index Manipulation and Angular Momentum Commutator Relations
I have been trying for hours and cannot figure it out. I am not asking anyone to do it for me, but to understand how to proceed.
We have the relations
$$[L_i,p_j] ~=~ i\hbar\; \epsilon_{ijk}p_k,$$
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16
votes
4answers
1k views
What symmetry causes the Runge-Lenz vector to be conserved?
Noether's theorem relates symmetries to conserved quantities. For a central potential $V \propto \frac{1}{r}$, the Laplace-Runge-Lenz vector is conserved. What is the symmetry associated with the ...
