d^2psi/dx^2=2m/hbar^2(V(x)-E) by studying the sign of the function and the second derivative for different values of E and V, which leads some graphs for function which behave well and the author makes some deductions from that. What buzzles me is the fact the equation is easily solved analytically, and the function will have two dinstict cases. one exponential if V>E and the second is complex when E<V.

Why would the author go through all this trouble instead of just solving the equation and in the case of complex function why even bother abouth trying to figure out the behaviour of the function psi, it have no physical meaning after all. anny comments would be appreciated