$y''(x) + (x^2 – \epsilon x^4 )y(x) = Ey(x)$ For the above differential equation,I need to find energy eigen state using perturbation theory.
Working : I solved the recursion relation,mainly considering anstaz relation and finally obtained $$2j(Bn,j) = (j + 1)(2j + 1)Bn,j+1 + Bn−1,j−2 − \sum[(Bn−k,1 Bk,j,when \,n=1,k=1)$$ But I am not sure how to code on mathematica and how the plot look likes.can anyone please advice me how to proceed or how the graph would be for negative coefficient?