I'm trying to reproduce the results of a paper. Somewhere (to explain a step of a procedure) the authors say:
Generate a set of orthogonal polynomials with the square of the Ground-state wave function as the weight function (WF) adopting any of the standard algorithms
Now I have the ground state wave function (GSWF) but I don't know how to use the above step and generate a set of orthogonal polynomials using the GSWF? I googled Orthogonal Polynomials and I just understood that it is possible to generate a set of orthogonal polynomials using Gram-Schmidt Orthonormalization for example, but I didn't understand how do so by my GSWF. If consider GSWF as $\psi_{gs}$ can anyone give me a simple procedure to generate a set of orthogonal polynomial with $\psi_{gs}$ as weight functions? Thanks in advance.
Using your given function as a starting point, you could generate first a set of complete functions. Let your weight function be $\phi^2_{gs}(x)$. We then construct the following set
$$S = \{x^n\phi^2_{gs}(x):n \in N\}$$
And now you can orthonormalise this set to get your orthogonal basis.