Checking units in particle in a box energy formula

[liquidFuzz]

In my book of formulas I have a formula for energy in different states, particle in box. $E_n = \frac{n^2 \pi^2 \hbar^2}{2ma^2}$

So I should get Joule or something here right. A quick look at the formula.

$E_n = \frac{n^2 \pi^2 \hbar^2 [Js]}{2m[kg]a^2 [m^2]} \frac{ [Js]^2}{[kg]* [m^2]}$ Becomes something like $\frac{J s^2}{m^2}$ After some rearrangement.

What am I missing..?

 

[bugatti79]

$$J= F[kg m/s^2]*d[m]=\frac{kgm^2}{s^2}$$

$$\implies [Js]^2= \frac{kg^2m^4}{s^2}\therefore \frac{[Js]^2}{kgm^2}=\frac{kgm^2}{s^2}=J$$