Responsible party: John Galt, Dark Helmet, Esquire

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<math> H_0|\psi_n^{(0)}>=E_n^{(0)}|\psi_n^{(0)}> </math>

<math> <\psi_m^{(0)}|\psi_n^{(0)}>=\delta_{mn} </math>

<math> H=H_0 +\lambda H' </math> ⇒ <math> H|\psi_n>=E_n|\psi_n> </math>

The goal is to seek an approximation of this new Hamiltonian expression. Specifically we want…

<math> E_n=E_n^{(0)}+\lambda E_n^{(1)}+\lambda^{2} E_n^{(2)} </math>

We define <math> <\psi_n^{(0)}|\psi_n^{(1)}>=<\psi_n^{(0)}|\psi_n^{(2)}>=0 </math>

A Fourier expansion can be used to express <math> |\psi_n^{(1)}>=\Sigma C_{mn}|\psi_n^{(0)}> </math> where m≠n

Plugging this into the new Hamiltion yields

<math> (H_0+\lambda H')(|\psi_n^{(0)}>+\lambda|\psi_n^{(1)}>)=(E_n^{(0)}+\lambda E_n^{(1)})(|\psi_n^{(0)}>+\lambda|\psi_n^(1)>) </math>

<math> H_0|\psi_n^{(0)}>+\lambda(H'|\p </math>

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