If I have a harmonic oscillator basis centered at $x=2$, how do I rewrite it in terms of the harmonic oscillator basis centered at $x=0$? To be more specific: If $|\Psi_n\rangle$ is the $n$th wavefunction centered at $x=2$, is there an expression for the coefficients $c_k$ in the following: $$ |\Psi_n\rangle = \sum_kc_k|\Phi_k\rangle, $$ where $|\Phi_k\rangle$ is the $k$th eigenstate for the harmonic oscillator at $x=0$.
The only thing I found related to this was squeezed states, which is related to changing frequencies, not the center.
