Please help me try to understand this problem. It deals with the quantum-confined Stark effect in nanoparticles.(adsbygoogle = window.adsbygoogle || []).push({});

For odd n, n = 1, 3, 5, ...

[tex]\psi_{n}(x) = \sqrt{\frac{2}{a}} \cos (\frac{n \pi x}{a})[/tex]

and for even n = 2, 4, 6, ...

[tex]\psi_{n}(x) = \sqrt{\frac{2}{a}} \sin (\frac{n \pi x}{a})[/tex]

and the zeroth order energy levels are

[tex]E_{n} = \frac{h^2 \pi^2 n^2}{2ma^2}[/tex]

The external field pertubation, H' = -qFx , where q is the charge and F is the applied electric field strength.

Now here's my work for the first order correction to the energy levels.

For odd n:

[tex]E_{n} = < \sqrt{\frac{2}{a}} \cos (\frac{n \pi x}{a})| H' | \sqrt{\frac{2}{a}} \cos (\frac{n \pi x}{a})> = 0[/tex]

For even n, I still get 0 for the first order correction. I just know that isn't right, and I think I know why:

Am I treating H' = -qFx correctly by assuming q and F are constants and x as the operator?

Thanks for the help. :shy:

**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!

# Perturbation Theory

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