expectation value of the ground state energy

Can you derive an expression for the uncertainty \(\Delta T\Delta\Phi\) between kinetic energy $T$ and potential energy \(\Phi\) for a quantum mechanical harmonic oscillator? Please keep in mind that the ground state fulfills the uncertainty relation exactly, \(\Delta p\Delta x = \hbar/2\).

bonus question: Can you bring in the virial relation \(\langle T\rangle = \langle\Phi\rangle\) and estimate the ground state energy?