I was computing an expectation value of kinetic energy. 

Here the kinetic energy is the square of momentum divided by 2m. 

But when I square expectation value of momentum, the textbook return Psi unsquared

Please see attachment. 

Your image cut off the top equation. Here is a hint the purpose to square the expectation value is to return a positive norm. All probability functions and energy densities are positive norm.

Edited July 1, 20205 yr by Mordred