Linked Questions
17 questions linked to/from What symmetry causes the Runge-Lenz vector to be conserved?
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Accidental degeneracy in Hydrogen Energies [duplicate]
The energy of Hydrogen electron ground state should depend on $n$ and $\ell$, but it only depends on $n$. What is the reason behind this accidental degeneracy; I know that the reason lies in symmetry; ...
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What symmetry operation mixes states with different $\ell$ in hydrogen atom? [duplicate]
We can mix states with different $m$ in hydrogen atom by rotating it around some axis (not coinciding with $z$). Thus rotation is the symmetry operation which mixes states with different $m$.
As ...
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Invariance of Lagrangian in Noether's theorem
Often in textbooks Noether's theorem is stated with the assumption that the Lagrangian needs to be invariant $\delta L=0$.
However, given a lagrangian $L$, we know that the Lagrangians $\alpha L$ (...
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Is there a kind of Noether's theorem for the Hamiltonian formalism?
The original Noether's theorem assumes a Lagrangian formulation. Is there a kind of Noether's theorem for the Hamiltonian formalism?
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Show that the Laplace-Runge-Lenz vector is conserved using poisson brackets
(I realise similar Phys.SE questions already exist but there is no answer with the Poisson bracket notation, I'll take this down if someone lets me know I should have commented in the existing ...
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Physical implication of conservation of Laplace-Runge-Lenz vector
I'm having trouble wrapping my mind around the Laplace-Runge-Lenz vector.
Conservation of momentum can be visualized as an object moving in a straight line with constant speed. One can even visualize ...
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Showing The Laplace–Runge–Lenz vector (per unit mass) is constant
Given an inverse square law $\ddot{\vec{r}}=-\frac{\mu}{r^2}\hat{r}$, I define the Angular momentum per unit mass as $\vec{H}=\vec{r}\times\dot{\vec{r}}$. Showing it's constant is strightfoward. Then ...
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What operator lowers the total angular momentum?
Assume states $|j,m\rangle$, say $j\in\{3,2,1,0\}$, initially at $3$.
Is there any "lowering" operator I could apply such that $L_-|j,m\rangle
=
|j-1,m\rangle
$?
How to express it in the $J_z$ ...
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Feynman's Lost Lecture: what is the significance of $\frac{d\mathfrak{v}}{d\theta}=-\frac{GMm}{\left|\mathfrak{L}\right|}\hat{\mathfrak{r}}?$
My question pertains to a fact used by Richard Feynman in his so-called
Lost Lecture. http://books.wwnorton.com/books/Feynmans-Lost-Lecture/.
I have only skimmed the book, so I have much more to learn ...
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Why are some symmetries invisible to the configuration space Lagrangian $L(q, \dot q,t)$?
Usually, when people talk about Lagrangians they are talking about a function of configuration space variables $q_i$ and their time derivatives $\dot q_i$. This is a function $L = L(q_i, \dot q_i,t)$. ...
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Component-free computation of Poisson bracket of Laplace-Runge-Lenz vector
How can the Poisson bracket $\{A,H\}$ be computed directly without components, where $H$ is the Hamiltonian for the inverse square force, $$H=\frac{p^2}{2m} - \frac{k}{|r|}\ ,$$
and $A$ is the ...
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Symmetry and Symplectic Group of Hydrogenic Atom
New version of the question:
A simmetry needs to be canonical, following the first answer of this post which states:
the symmetry requirement is not necessary in the definition of canonical ...
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Example of a classical action changing by a nonzero boundary term under a continuous transformation
Is there an example of a continuous transformation in classical field theory under which the classical action changes by a nonzero boundary term? I'd prefer an example from field theory in flat ...
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Physical interpretation of the symmetry for the Runge-Lenz vector
In the post What symmetry causes the Runge-Lenz vector to be conserved?, and based on the results of https://arxiv.org/abs/1207.5001, it was it was discussed that the Runge-Lenz vector is the ...
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Legendre transformation and correspondance between Noether charges and quasi-symmetries
I have been trying to understand the Legendre transformation (in mechanics, in the hyperregular case: when the Legendre transformation is one-to-one) and the correspondence between symmetry $\to$ ...
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