Hamiltonian vs. Energy
- From: Pmb <someone@xxxxxxxxxxxxx>
- Date: Tue, 11 Mar 2008 14:34:57 +0000 (UTC)
I was wondering if anyone knows of systems for which the Hamiltonian is not
equal to the total energy? This is an interesting problem in analytic
mechanics (e.g. Lagrangian and Hamiltonian dynamics) but is rarely, if ever,
mentioned in forums and newsgroups. I'd love to see a large set of examples
for which this is true. I'd like to get an intuitive feeling for when the
Hamiltonian equals the energy. I'm also interested in the Hamiltonian for a
object sliding on plane with only gravity and friction acting on the body.
Seems to me that there is a Lagrangian equation for this but that the
associated Lagrangian does not account for the energy lost to friction and
as such Hamiltonian does not account for this. I'm also very interested in
whether there are quantum mechanical systems for which the Hamiltonian is
not the energy. All input, references, thoughts and comments are welcome.
There is an example of this in Classical Mechanics - Third Ed., by
Goldstein, Safko and Poole page 345-346. Thank you.
Best wishes
Pete
.
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