# Expectation value of kinetic energy

1. Dec 4, 2013

### White_M

1. The problem statement, all variables and given/known data

Given the following hypothetic wave function for a particle confined in a region -4≤X≤6:

ψ(x)= A(4+x) for -4≤x≤1
A(6-x) for 1≤x≤6
0 otherwise

Using the normalized wave function, calculate the expectation value of the kinetic energy.

2. Relevant equations

I used ∫ψ*ψdx=1 to normaize the function and got that |A|^2=3/250.

3. The attempt at a solution
I know that T=$\frac{\hat{P^2}}{2m}$=$\frac{-h^2}{2m}$$\frac{d^2}{dx^2}$
I tried to calculate it using <T>=∫ψ*Tψ using the expression above and got zero which is not correct.

The solution given by the book is <T>=-$\frac{h^2}{2m}$$\frac{3}{250}$(0*1-5*2+0*1)=$\frac{3h^2}{50m}$

p.s
h in the formulas above is $\frac{h}{2pi}$

What am I doing wrong?

Thanks. Y.

2. Dec 4, 2013

### clamtrox

The second derivative is not zero everywhere.