Take the tour ×  In which condition, the Hamiltonian is the same
as the total energy of the system, or say $H=T+V$?
share|improve this question OP's question(v1) asks precisely the
opposite of this Phys.SE question. –  Qmechanic Oct 31 '12 at
17:54 add comment  3 Answers  The Hamiltonian in a conservative
system describes the total internal energy of the system.  The
formula $H=T+V$ with the traditional form of the kinetic energy
is valid for a frictionless nonrelativistic system in Cartesian
coordinates, possibly with external forces.  share|improve this
answer add comment  The Hamiltonian is a constant of the motion
as long as it is independent of time. More deeply that means
that the Lagrangian it comes from must be independent of time.
A constant Hamiltonian is the total energy if the potential is
velocity independent.  share|improve this answer But $H=T+V$
also holds for a forced harmonic oscillator, where $H$ is not a
constant of the motion. –  Arnold Neumaier Nov 1 '12 at 14:09
add comment  By defini