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 obt
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