English related question about quantization and separation of variables

I’m not a native speaker, and this question is about "how to say it in English".
Consider a 2D electronic waveguide. Wavefunction $psi(x,y)$ can be written in form of separated variables $psi(x,y)=U(x)V(y)$.
Now we add boundary conditions related to $y$-axis. Spectrum of $V(y)$ becomes discrete with energies $E_n$.
How to describe this in English? Can I say "$y$-quantization" about the operation I do, and "$n$ is a $y$-quantum number" about the $n$?