In quantum mechanics, Hamiltonian is a considerable measurement, which corresponds to the total energy of the system. ▽ itself is meaningless, it is an operator, and at the same time it is regarded as a vector, which has the dual identity of vector and differential when operating.
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Time evolution of quantum states generated by hamiltonian operators. What if there is time? t？ System status, where? Reduce Planck's constant. This equation is the Schrodinger equation. It has the same form as Hamilton-Jacobian equation, hence the name Hamilton.
If the state of the system is given at the initial moment (t=0), we can get the state of the system at any subsequent moment through integration. In particular, if? Independent of time, the form of steady-state solution remains unchanged.