Proving Parity in Normalized Solutions of the Schrodinger Equation

[ProfessorChaos]

Hopefully this is in the correct section.

Struggling with this question though I don't think it should be particularly difficult:

Show that if V(x) = V(-x) normalised solutions to the time-independent Schrödinger equation have definite parity - that is, u(x) = +-u(-x)

(+- means plus or minus. Sorry for poor formatting - on phone)

Thanks in advance.

 

[ProfessorChaos]

Just read the "how to ask for help" sticky.

My attempt at a solution involved subbing y = -x. Obtaining a solution, then trying to normalise it. However I don't get anywhere really, and my line of argument through my current page of working reads unconvincing (I'm just guessing).

Cheers