Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with laplace-runge-lenz-vector
Search options answers only
not deleted
user 2451
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.
3
votes
Index Manipulation and Angular Momentum Commutator Relations
It is possible to continue OP's calculation as follows
$$ =~i\hbar\; \epsilon_{jmn}(\epsilon_{ink}p_m L_k+\epsilon_{imk}p_k L_n)
~=~-i\hbar( \epsilon_{jkm} \epsilon_{min}+\epsilon_{kim} \epsilon_{mj …
- 213k
37
votes
Accepted
What symmetry causes the Runge-Lenz vector to be conserved?
Hamiltonian Problem. The Kepler problem has Hamiltonian
$$\begin{align} H~=~&T+V, \cr
T~:=~& \frac{p^2}{2m}, \cr
V~:=~& -\frac{k}{q}, \end{align}\tag{1} $$
where $m$ is the 2-body reduced mass. The …
- 213k
2
votes
Textbook proof error? Runge Lenz
They say that $\vec{r} \cdot \dot{\vec{r}} = |\vec{r}|\frac{d}{dt}|\vec{r}|,$ not that $\vec{r} \cdot \dot{\vec{r}} = |\vec{r}||\frac{d}{dt}\vec{r}|.$
- 213k
3
votes
How is angular momentum defined on symplectic space?
In the Kepler-problem, note that only 5 of the 6 integrals of motion $(\vec{L},\vec{B})$ are algebraically independent, since $\vec{L}\cdot \vec{B}\equiv 0$. They parametrize a 5-dimensional submanifo …
- 213k
23
votes
Why are hydrogen energy levels degenerate in $\ell$ and $m$?
The degeneracy of energy-levels can be traced to the fact that the hydrogen atom possesses an enhanced $SO(4)$ symmetry caused by (among other things) the conservation of the Laplace-Runge-Lenz vector …
- 213k
3
votes
Conserved Quantities in Kepler Problem?
He could (and should) count the mechanical energy as a conserved quantity. He also didn't mention that the total momentum of the 2 objects is 3 integrals of motion. However, not all quantities are in …
- 213k