I have a computational project to do for quantum, and I am kind of tired of doing basic barriers, so I decided to try a quadratic barrier. Well, you get garbage. However, since I'm working with numerical approximations anyways, I figured I might try it, but I am not sure how to proceed. Here is what wolfram gives me: http://www.wolframalpha.com/input/?i=-h^2/(2*m)*y''+++x^2*y+=+k*y Note: k == Energy, I just used k because it changed E -> e. If you scroll down and see the solution, it is in terms of the parabolic cylinder function D which is the solution to weber equations. https://en.wikipedia.org/wiki/Parabolic_cylinder_function I am not really getting what to do with this. I'm not sure on the notation used, and the link is no help. https://en.wikipedia.org/wiki/Abramowitz_and_Stegun Can someone give me advice on how to numerically approximate this function?