Hamiltonian Operator

An operator corresponding to the total energy of that system, including both kinetic energy and potential energy.

$\hat{H}=\hat{T}=+\hat{V}$ Where $\hat{V}$ is the potential energy operator and $\hat{T}$ is the kinetic energy operator.
$\hat{T}=\frac{\hat{\mathbf{p}}\cdot \hat{\mathbf{p}}}{2m}=\frac{{\hat{p}}^2}{2m}=-\frac{{\hslash }^2}{2m}{\nabla }^2$
in which $m$ is the mass of the particle, the dot denotes the dot product of vectors, and
$\hat{p}=-i\hslash \nabla$, is the momentum operator where ${\nabla }^2$ is the Laplacian Operator .