Can this be a Hamiltonian Evolution?

[atomqwerty]

Homework Statement

Let be [itex]q(t)=e^{-t}\alpha[/itex] and [itex]p(t)=e^{-t}\beta[/itex]

Can this be a Hamiltonian Evolution

Homework Equations

The Hamilton equations for [itex]\dot{p}[/itex] and [itex]\dot{q}[/itex].

The Attempt at a Solution

Can be a Hamiltonian evolution if verifies Hamilton equations:

[itex]\dot{p}=-e^{-t}\alpha[/itex]

[itex]\dot{q}=-e^{-t}\beta[/itex]

but I get to a loose end...
Thanks!

 

[mark726]

Dear fellow scientist,

Yes, this can indeed be a Hamiltonian evolution. In order to verify this, we can use the Hamilton equations for \dot{p} and \dot{q}, as mentioned in the homework equations. We can see that \dot{p}=-e^{-t}\alpha and \dot{q}=-e^{-t}\beta, which are the same as the expressions given in the problem. This means that the Hamilton equations are satisfied, and therefore this can be considered a Hamiltonian evolution.

I hope this helps! Good luck with your research.