Hamiltonian total energy Planck constant classical Hamiltonian correspondence principle energy
Here 



H


{\displaystyle H}

 denotes the Hamiltonian, the observable corresponding to the total energy of the system, and 



ℏ


{\displaystyle \hbar }

 is the reduced Planck constant. The constant 



i
ℏ


{\displaystyle i\hbar }

 is introduced so that the Hamiltonian is reduced to the classical Hamiltonian in cases where the quantum system can be approximated by a classical system; the ability to make such an approximation in certain limits is called the correspondence principle.
