- #1
terp.asessed
- 127
- 3
Homework Statement
Calculate <K>, the expectation value of the kinetic energy for the ground state of a pair of vibrating nuclei (assume internuclear distance--hence -infinite to +infinite)
Homework Equations
K = -h2/2(mu) d2/dx2
where (mu) = reduced mass; m1m2/(m1+m2)
and
wave(x) = (a/pi)1/4 e(-ax2/2)
where a = (mu) (omega)/h
(Assume h = Planck's constant with dash)
The Attempt at a Solution
<K> = integral (x = -infinite to infinite) wave2(x) K(x) dx
= integral (a/pi)1/2 e(-ax2) -h2/2(mu) d2/dx2 dx
= -ah2/(2pi(mu)) integral e(-ax2) -h2/2(mu) d2/dx2 dx
= -a5/4h2/(2pi5/4(mu)) integral {-ae-3ax2/2 + a2x2e(-3ax2/2)}dx
...beyond, I don't know how to simplify the integral--have I done something wrong in the midway? I don't know how to integrate anymore. Any suggestions would be welcome!