Show that a dipole operator of the form, $$\hat \mu=\mu_0\hat x$$ can lead to a transition between two levels in the 1D particle in a box.
How deos a dipole operator of the form $$\hat\mu=\mu_0\hat r=\mu_{0,x}\hat x +\mu_{0,y}\hat y$$ affect eigenfunctions of degenerate energy states of the 2D particle in a box? Can it interconvert these states?