Please help me try to understand this problem. It deals with the quantum-confined Stark effect in nanoparticles.
For odd n, n = 1, 3, 5, ...
\psi_{n}(x) = \sqrt{\frac{2}{a}} \cos (\frac{n \pi x}{a})
and for even n = 2, 4, 6, ...
\psi_{n}(x) = \sqrt{\frac{2}{a}} \sin (\frac{n \pi x}{a})
and...