5
votes
Accepted
Is this hamiltonian of the form of some well-known physical system?
One likely candidate for what they "want you to say" is a Kepler potential (i.e. produced by an inverse distance-squared force) viewed in a rotating frame that scales the rotation rate by a ...
- 1,277
4
votes
What is the correct general form of Hamilton's equation?
Most generally the observable $F$ depends not only on $q(t)$ and $p(t)$,
but also depends on $t$ explicitly, i.e.
$$F=F(q,p,t)$$
Differentiating this with respect to time $t$ you get
$$\begin{align}
\...
- 25.9k
2
votes
Accepted
Would it be more insightful to teach students Lagrangian/Hamiltonian mechanics before Newtonian mechanics?
The concept of energy comes with luggage.
Potential energy does not have an intrinsic zero point. If you have two position coordinates then what is definable is the potential difference between the ...
- 15.2k
1
vote
Accepted
Finding a new hamiltonian from a given canonical transformation
Since you know the new $q(Q)$, it’s easier to use another generating function $F(p,Q)=pq(Q)$ (Legendre transform of your function) which gives:
$$
q = \frac{\partial F}{\partial p}(=q) \\
P = \frac{\...
- 1,182
1
vote
Accepted
Can a primary constraint contain spatial derivative of the field?
Yes, in field theory the primary constraints can contain spatial$^1$ derivatives of the canonical fields.
One example is when Legendre transforming the Nambu-Goto (NG) string action, see e.g. this ...
- 167k
1
vote
Spin Orbit Coupling Hamiltonians
No, these are not always the same thing.
Spin-orbit coupling in atoms
Spin-orbit coupling can be derived by reduction of the Dirac equation to non-relativistic limit, as one of several relativistic ...
- 37.4k
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