quantum mechanics - Coupled Harmonic Oscillator - Solve by diagonalization

I have a problem where I have two massive Particles $M$ and one particle with mass $m

This probably means to switch to new coordinates \begin{equation} y_1 = -q_1+q_2\\ y_2 = -\frac{1}{\sqrt{2}}q_1-\frac{1}{\sqrt{2}}q_2+q_3\\ y_3 = \frac{1}{\sqrt{2}}q_1+\frac{1}{\sqrt{2}}q_2+q_3 \end{equation}

But what do I do with the momentum operators. They should change accordingly but I am confused as to how exactly