I have a problem where I should calculate the ground state eigenfunction of a particle in the box where the potential V(x)=0 when 0<x<L and infinite everywhere else with the perturbation [itex]V'(x)=\epsilon[/itex] when L/3<x<2L/3.(adsbygoogle = window.adsbygoogle || []).push({});

I get that the total ground state eigenfunction with the first order perturbation contribution is

[tex]

u_{1}=u_{01}+{\int_{L/3}^{2L/3} {u_{02}\hat H' u_{01}dx} \over (E_{01}-E_{02})}u_{02}+{\int_{L/3}^{2L/3} {u_{03}\hat H' u_{01}dx} \over (E_{01}-E_{03})}u_{03}

[/tex]

where

[itex]

\hat H'=\epsilon}[/itex] and [itex]u_{0n}/E_{0n}=[/itex] eigenfunctions/energies of the unperturbed system.

I only need to use [itex]\{u_{01},u_{02},u_{03}\}[/itex] instead of all [itex]\{u_{0n}\}[/itex] when expressing the first order perturbation contribution

[tex]u_{11}=\sum_k a_{nk}u_{0k}[/tex]

Is this correct?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Perturbation theory?

**Physics Forums | Science Articles, Homework Help, Discussion**