Energy operator
In quantum mechanics, energy is defined in terms of the energy operator, acting on the wave function of the system as a consequence of time translation symmetry. == Definition == It is given by: E ^ = i ℏ ∂ ∂ t {\displaystyle {\hat {E}}=i\hbar {\frac {\partial }{\partial t}}} It acts on the wave function (the probability amplitude for different configurations of the system) Ψ ( r , t ) {\displaystyle \Psi \left(\mathbf {r} ,t\right)} == Application == The energy operator corresponds to the full energy of a system.