Perturbation Theory
#Physics
Quantum Physics
Topics
$\displaystyle E_{n}^{1}=\braket{ \psi_{n}^{0} | H'| \psi_{n}^{0} }$
- First order correction to energy
- $\displaystyle H'$ is the perturbation
- $\displaystyle \psi_{n}^{0}$ is the unperturbed state
$\displaystyle \psi_{n}^{1}=\sum_{m \neq n}^{} \frac{\braket{ \psi_{m}^{0}|H' | \psi_{n}^{0} }}{(E_{n}^{0}-E_{m}^{0})}\psi_{m}^{0}$
- First-order correction to wave function of perturbation
$\displaystyle E^{2}{n}=\sum{m \neq n}^{} \frac{\lvert \braket{ \psi_{m}^{0}|H' | \psi_{n}^{0} }\rvert^{2}}{E_{n}^{0}-E^{0}_{m}}$
- Second order correction to energy