Background: In this problem you will prove that the Heisenberg
Uncertainty Principle (HUP) follows directly from the operator
formalism which we developed from the de Broglie hypothesis!!! You
may regard this proof as either one confirmation that our formalism is
consistent with our experimental observations of the HUP or as the
precise mathematical link between the Davisson-Germer/G.P. Thomson
observations that 
and the HUP statement that 
.