Solution
= Solution
The unperturbed <Hamiltonian> satisfies
$$
\boxed{\hat H^{(0)}\Psi_i^{(0)}=E_i^{(0)}\Psi_i^{(0)}.}
$$
The supplied <eigenfunctions> can be chosen as an <orthonormal eigenbasis>, with $\langle\Psi_j^{(0)}|\Psi_i^{(0)}\rangle=\delta_{ji}$.