Im not sure how to start or where the equation came from. Suppose a particle is

Question

Im not sure how to start or where the equation came from.

Suppose a particle is in the ground state (n = 1) of an in finite potential energy well. The energy is E_1 = h^ pi^2/2mL^2) = K + U = K because U= 0. Thus -r = or p, = Thus h^2pi^2/2mL^2=p^2_x/2m or P_x = hpi/L If p_x is exactly known, then Deltap_x = 0. For this problem, Deltax = L (the particle is known to be somewhere in that interval). We then obtain Deltax Deltab_x = (L)(0) = 0, in violation of the uncertainty principle. WHAT'S WRONG WITH THIS CALCULATION???

Explanation / Answer

As long as the particle is confined within the box, one can not measure momenttum with with perfect accuracy. To measure momentum with perfect accuracy, one will need an apparatus much bigger than the box and that will not confine the particle to the box and uncertanity in the position will be greater than the zize of the box.

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