Numerical Solution
Divide the range of x into intervals of width ?x
denote discrete positions as xs = s ?x
denote ?s = ?(xs) and ?`s = ?`(xs)
if the potential V(x) satisfies V(-x)=V(x) then the solution have definite parity: even or odd
choose ?(0)=1 and ?`(0)=0 for even parity
choose ?(0)=0 and ?`(0)=1 for odd parity
compute ?`s+1 and ?s+1 using the algorithm