Kinetic Energy

#Physics
Often represented with either a $\displaystyle K$ or $\displaystyle T$

Classical

$\displaystyle K=\frac{1}{2}mv^{2}$

$\displaystyle K=\frac{p^{2}}{2m}$

$\displaystyle K=\frac{3}{2}\tau$

• Kinetic energy of a particle
• $\displaystyle \tau$ is the fundamental temperature

Quantum

$\displaystyle \hat{K}=- \frac{\hbar ^{2}}{2m}\frac{ \partial ^{2} }{ \partial x^{2} }$

$\displaystyle {\left\langle{K}\right\rangle}=-\frac{\hbar ^{2}}{2m}\nabla=\int \Psi^{*}\frac{ \partial ^{2}\Psi }{ \partial x^{2} } , \mathrm{d}x$