Mathematically, this role can be played by any smooth, real-valued function on a symplectic manifold, and those quantities wh
Mathematically, this role can be played by any smooth, real-valued function on a symplectic manifold, and those quantities whose Poisson bracket with it is zero are conserved over time. In quantum mechanics, when a non-trivial unitary operator commutes with this quantity, degeneracy will occur, and this quantity can also be written as "minus i times h-bar times the partial derivative with respect to time of the wave function." Appearing in the Schrodinger equation for finding eigenstates and obtained by a Legendre transform from the Lagrangian, for ten points, identify this physical quantity which represents a system's total energy.
Mathematically, this role can be played by any smooth, real-valued function on a symplectic manifold, and those quantities whose Poisson bracket with it is zero are conserved over time.
Hamiltonian