For a charged particle, this function includes the square of the difference of the momentum and e over c times the vector pot
For a charged particle, this function includes the square of the difference of the momentum and e over c times the vector potential. Any quantity whose Poisson bracket or commutator with it is zero is also a constant of the motion, and in quantum mechanics, the eigenvalues of this operator are the allowed energies. Equal to the Legendre transform of the Lagrangian, FTP name this function named for the inventor of quaternions, who also lends his name to closed circuits that touch each node of a graph once.
For a charged particle, this function includes the square of the difference of the momentum and e over c times the vector potential.
Hamiltonian