Perturbation Theory

Quantum Physics

Topics

• Feynman-Hellmann Theorem

$E_n^1=⟨{\psi }_n^0|H^{\prime }|{\psi }_n^0⟩$

• First order correction to energy
• $H^{\prime }$ is the perturbation
• ${\psi }_n^0$ is the unperturbed state

${\psi }_n^1=\sum _{m\ne n}\frac{⟨{\psi }_m^0|H^{\prime }|{\psi }_n^0⟩}{(E_n^0-E_m^0)}{\psi }_m^0$

• First-order correction to wave function of perturbation

$E_n^2=\sum _{m\ne n}\frac{|⟨{\psi }_m^0|H^{\prime }|{\psi }_n^0⟩{|}^2}{E_n^0-E_m^0}$

• Second order correction to energy