Evaluate the average of the square of the linear momentum of the quantum harmonic oscill...

Evaluate the average of the square of the linear momentum of the quantum harmonic oscillator for the ground state (n = 0) and first two excited states (n = 1 and n = 2). Use the hint about evaluating integrals in Problem P18.12.

Reference problem 18.12

Show by carrying out the appropriate integration that the total energy eigenfunctions for the harmonic oscillator are orthogonal over the interval -∞ < x < ∞ and that is normalized over the same interval. In evaluating integrals of this type, if f (x) is an odd function of x and if f (x) is an even function of x.