How to determine correct sign for a numerical solution to a differential equation?
Hello! Recently just wrote a program in Python to numerically solve the radial portion if the hydrogen atom using Numerov's method and it led me to a question I am curious about. I can obtain correct normalized solutions when comparing to solutions constructed by using Scipys associated Laguerre polynomials. However my solutions are sometimes flipped by a negative sign.
If I am given a random wave functions numerical differential equation to solve, is there a way to determine if it has the correct sign?
I want to say it doesnt matter since measurements deal with the squares of the solutions, but if I look at other results online my solutions are sometimes flipped about the domains axis. It makes me wonder if there are tests I should be doing to negate this.