Kinetic energy

• $\frac{1}{2}m{v}^2$ for a classical Particle
• $\hat{T}=-\frac{\hslash }{2m}{\nabla }^2$ for a Quantum state.

In the above

• $m$ is the mass
• $v=\dot{x}$ is the velocity
• $\hslash$ is Planck’s reduced constant
• ${\nabla }^2$ is the Laplacian