The ground state wave-function of a 1-D harmonic oscillator is
$$
\psi(x) = \sqrt\frac{a}{\sqrt\pi} * exp(-\frac{a^2*x^2}{2}\frac{i\omega t}{2}).
$$
a) find Average potential energy ?
$$
\overline{V} = \frac{1}{2} \mu\omega^2\overline{x^2}
$$
b) find Average kinetic energy ?
$$
\overline{T} =...