Schrodinger Equation

In the Schrodinger picture, the equation governing quantum mechanical evolution of some state $\Psi$ in the relevant Hilbert space is given by $i\hbar\partial_t\Psi = \hat{H}\Psi$ , where $\hat{H}$ is the linear operator representing the Hamiltonian, usually of the form $-\frac{\hbar^2}{2m}\Delta + V$ where $\Delta$ is the relevant Laplace(-Beltrami) operator.