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## Main Question or Discussion Point

Hi all. I have been thinking about a very simple question, and I am a little confused. We know from time-independent perturbation theory that if the system is perturbed by the external perturbation λV which is much smaller compared to the unperturbed hamiltonian H0, we can write the ground state wave function and the ground state energy as a power series in the parameter λ. So that makes the time-independent Shcoringer to be:

[H0 + λV] [ψ0 + λψ1 + ...] = [E0 + λE1 + ...] [ ψ0(t) + λψ1 + ...]

where ψ0 and ψ1 are respectively the unperturbed and the first-order perturbed wave functions. Now my question is, can we also write the

(ih/2π) ∂/∂t [ψ0(t) + λψ1(t) + ...] = [H0 + λV] [ ψ0(t) + λψ1(t) + ...]

= [E0 + λE1 + ...] [ ψ0(t) + λψ1(t) + ...]

Thanks guys.

[H0 + λV] [ψ0 + λψ1 + ...] = [E0 + λE1 + ...] [ ψ0(t) + λψ1 + ...]

where ψ0 and ψ1 are respectively the unperturbed and the first-order perturbed wave functions. Now my question is, can we also write the

__Time-dependent__Schrodinger equation of this system as(ih/2π) ∂/∂t [ψ0(t) + λψ1(t) + ...] = [H0 + λV] [ ψ0(t) + λψ1(t) + ...]

= [E0 + λE1 + ...] [ ψ0(t) + λψ1(t) + ...]

Thanks guys.