At time \(t=0\), the ground state wavefunction of a one-dimensional quantum harmonic oscillator with potential \(V(x)=\frac{1}{2} m \omega_{0}^{2} x^{2}\) is given by

\[
\psi(x, 0)=\frac{1}{\pi^{1 / 4} \sqrt{a}} \exp \left(-\frac{x^{2}}{2 a^{2}}ight)
\]

where \(a=\sqrt{\frac{\hbar}{m \omega_{0}}}\). At \(t=0\), the harmonic potential is abruptly removed. Use the momentum representation of the wavefunction at \(t=0\) and the time-dependent Schrodinger equation to determine the spatial wavefunction and density at time \(t>0\); compare to equation (7.2.11).