# Energy for a non-relativistic particle equation

1. Oct 20, 2012

### ZedCar

I have an equation for a non-relativistic particle, in relation to quantisation of a particle in a box, which states:

E = (p^2 / 2m) = {(n^2 h^2) / (8 m a^2)}

Should the 'h' (Plancks constant) in this equation be h-bar ?

Thanks.

2. Oct 22, 2012

### Mark M

If you wish to write the energy levels with $\hbar$, then the equation will look like this $$E = \frac {n^{2} \hbar ^{2} \pi^{2}} {2m a^{2}}$$ The two expressions are equivalent. The way the equation is derived is by using the relation $p =\hbar k$, substituting in $k = \frac {n \pi} {a}$ and then substituting it into $E = \frac {p^{2}} {2m}$.