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Energy for a non-relativistic particle equation

  1. Oct 20, 2012 #1
    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. jcsd
  3. Oct 22, 2012 #2
    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}##.
     
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