A particle in one dimension is in an infinite potential well between \(\frac{-L}{2} \leq x \leq \frac{L}{2}\). For a perturbation \(ϵ \cos \left(\frac{\pi x}{L}\right)\) where ϵ is a small constant, the change in the energy of the ground state, to first order in ϵ, is
1
\(\frac{5 \epsilon}{\pi}\)
2
\(\frac{10 \epsilon}{3 \pi}\)
3
\(\frac{8 \epsilon}{3 \pi}\)
4
\(\frac{4 \epsilon}{\pi}\)