kinetic energy expectation value

this post is related to things we will cover in the future.
I think that for H2+ the integrand for the kinetic energy expectation value is:
\( \psi_m (\vec{r})(\frac{-\hbar^2}{2m})\bigtriangledown^2 \psi_m (\vec{r})\)
where,
\( \psi_m( \: \vec{r}) = \frac{c_m(b)}{\sqrt{2}} ( \psi_{1s} (r) + \psi_{1s}(\:\vec{r}-b \hat{x})) \)
where b is the distance between the two protons.

Note that \(c_m(b)\) is a function of b, is close to 1 for most values of b, and is unit-less. It has to be evaluated by a normalization integral for each value of b.

Also, one can turn hbar^2/m into a simple fixed number, which is easier to use in numerical calculation, using:
\(\hbar^2/m = .076 \:eV nm^2\)