All Questions
6
questions
1
vote
1
answer
54
views
Sufficient condition for conservation of conjugate momentum
Is the following statement true?
If $\frac{\partial \dot{q}}{\partial q}=0$, then the conjugate momentum $p_q$ is conserved.
We know that conjugate momentum of $q$ is conserved if $\frac{\partial L}{\...
- 41
0
votes
1
answer
55
views
Which is the differential $\text{d} p_i$ of a generalized momentum?
I want to get a partition function, but I introduce a generalized momentum, my doubt is about, when I define a differential respect to $p$, it means $\text{d} p$, which is the correct form to get it?
...
- 13
2
votes
2
answers
161
views
Conjugate momentum notation
I was reading Peter Mann's Lagrangian & Hamiltonian Dynamics, and I found this equation (page 115):
$$p_i := \frac{\partial L}{\partial \dot{q}^i}$$
where L is the Lagrangian. I understand this is ...
- 41
5
votes
4
answers
924
views
Partial derivative in Newtons Second law
Newton's second law states Force is the time derivative of momentum. But is it a total derivative or partial derivative? What is the reason behind it?
- 53
0
votes
1
answer
943
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
2
votes
1
answer
443
views
What is the function type of the generalized momentum?
Let
$$L:{\mathbb R}^n\times {\mathbb R}^n\times {\mathbb R}\to {\mathbb R}$$
denote the Lagrangian (it should be differentiable) of a classical system with $n$ spatial coordinates. In the action
$...
- 8,523