Normalizing a piecewise electron wave function

[psingh]

Homework Statement

Consider the electron wave function where x is in nm:

psi(x)=cx |x|<= 1nm & c/s |x| => 1 nm

Determine the normalization constant c

Homework Equations

integral(|psi(x)|^2) dx=1 between infinity and negative infinity

The Attempt at a Solution

this may be very far from the real solution but this is what I've tried

integral{ (cx)^2 dx + (c/x)^2 dx}

1= integral { (c^2x^2) + (c^2/x^2) }

c^2 integral{ x^2 + x^-2 }

(x^3/3 - 1/x)*c^2=1

integral{ x^3/3 - 1/x }

im not quite sure where to go from here

 

[Dick]

You need to split the integral into two parts, one for |x| in 0-1 nm, the other from |x| in 1 nm to infinity. Then add them.