The kinetic energy operator, denoted by (-\frac{\hbar^2}{2m}\nabla^2), is a mathematical operator that represents the kinetic energy of a particle in quantum mechanics. It operates on the wavefunction of the particle, which describes its state, and returns a value that is proportional to the particle’s kinetic energy. The kinetic energy operator is related to the momentum operator, (\hat{p}=-i\hbar\nabla), through the following equation: (\hat{p}^2=2m\hat{T}).
