All Questions
Tagged with covariant-derivatives or differentiation
259 questions
0
votes
1
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515
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What is the $d/dt$ in the Schrödinger equation? [duplicate]
I'm wondering, in the Schrödinger equation,
$$
{\displaystyle i\hbar {\frac {d}{dt}}\vert \Psi\rangle ={\hat {H}}\vert \Psi }
$$
what is the $
{\displaystyle {\frac {d}{dt}}}
$ ? I understand it has ...
- 103
0
votes
1
answer
55
views
Exponentiation of linear combination of commuting Vector fields
I have to prove the formula:
$$e^{a\partial/ \partial\lambda +b \partial / \partial\mu}=e^{a\partial/ \partial\lambda}e^{b\partial/ \partial\mu}$$
if $\partial/ \partial\lambda$ and $\partial/ \...
- 1,518
0
votes
1
answer
1k
views
Squaring the momentum operator in QM becomes a second derivative. How?
$\frac{p^2}{2m}$ is the Kinetic energy in classical mechanics. However, the same $p^2$ becomes the second derivative $\frac{\partial ^2}{\partial x^2}$ in the Kinetic Energy operator in QM. I mean it ...
- 21
0
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1
answer
397
views
Killing equation in coordinates
In proving that it is possible to write the killing equation in coordinates as $$L_X g=0\iff X_{\alpha;\beta}+X_{\beta;\alpha}=0$$
I have read that the key observation, to write the equation in ...
- 187
-1
votes
1
answer
340
views
Could you give me an application on physics of Gauss Divergence Theorem for scalar? [closed]
Gauss divergence theorem for vectors can be easily explained by mass balance. But I can't think about one example for scalar gauss divergence theorem.
Gauss Divergence Theorem for scalars:
$$\int\...
- 109
-1
votes
3
answers
493
views
The use of the commutators in quantum mechanics: explanations [duplicate]
Considering that I've never studied quantum mechanics before I have need to understand the operator commutator. My start is: $[A,B]=AB-BA \tag{a}$
Now, why must be
$$\left[\frac{\partial }{\partial ...
- 2,575
-1
votes
1
answer
96
views
Finding solution to this differential equation
In this paper http://arxiv.org/abs/hep-th/9506035 equation (3.11) was written as: $$\frac{\partial L}{\partial u}\frac{\partial L}{\partial v} = -1$$
The author then said p.9 that "approximate ...
- 215
-1
votes
1
answer
4k
views
Lennard-Jones potential, distance $r$ for minimum energy
I'm sorry if the question seems stupid. I found (wikipedia) that the Lennard-Jones potential has it's minimum at a distance of
$$r = 2^{\frac{1}{6}}\sigma.$$
If $U(r)_{min} = -\epsilon$
$$U(r) = 4\...
- 137
-2
votes
3
answers
2k
views
Curl of a vector field [closed]
What is the physical interpretation of curl of a vector field? Just as divergence implies flux through a surface.
I mean if $\vec A$ is a vector field, what does $\left(\nabla \times \vec A \right)$ ...
- 4,984