Is There a Canonical Transformation for x = 2qa/sin(T) and p = 2qa.cos(T)?

  • Thread starter Thread starter photomagnetic
  • Start date Start date
  • Tags Tags
    Transformations
photomagnetic
Messages
13
Reaction score
0

Homework Statement


Show that x = 2qa/sin(T) and p = 2qa.cos(T) is a canonical transformation
into new coordinates T and momentum q.

Homework Equations

The Attempt at a Solution


It looks easy, I've tried matrix/jacobi method, and symplectic method. But these two seem to be not canonical. Am I missing something? The question doesn't give anything else. Do I have to find a generating function to prove that they are canonical? But then it'd would be silly, because the professor is very clear about these things. If he wanted to see a F generating function he would have said so.
 
Physics news on Phys.org
Clue: do you have any theorems that provide necessary and sufficient conditions for a transformation to be canonical?
 
I re-correct myself, the prof. is an jerk. He hadn't mentioned that we had to use a generating function. now I got it. thanks anyway.
 
That's not nice. I'm sure your prof is a very nice fellow.

Incidentally, there are several different methods that you might have used to show that the given transformation is canonical.
 
Yeah not telling which method we "must" use is not nice either.
Anyway after trying to do 3 hws each week, and spending a huge chunk of time,
people can get mad. Also no need to be politically correct here.
 

Thread 'Please tell me where I am going wrong in this integral'

##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
View full post »

Thread 'Direction of the magnetic field of an oscillating charge'

Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
View full post »

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
View full post »

Similar threads

Canonical transformations of a quantized Hamiltonian?
Replies
3
Views
1K
I Canonical transformation from canonical to kinetic momentum
Replies
7
Views
1K
How can I determine the values of α and β for a canonical transformation?
Replies
19
Views
2K
Given a set of equations, show if it is a Hamiltonian system
Replies
9
Views
2K
Spring with oscillating support (Goldstein problem 11.2)
Replies
7
Views
2K
General Form of Canonical Transformations
Replies
3
Views
2K
Canonical Transformation / Poisson Brackets
Replies
3
Views
3K
Finding the generator of a transformation
Replies
1
Views
3K
Order of steps on Hamiltonian canonical transformations
Replies
1
Views
2K
How can I use Poisson bracket to find P in a canonical transformation?
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top