Problem Set 7


Due November 6


I.          Consider the wavefunction y(x) = Cexp(-x2/a2).

            a.  Determine the normalization constant C.

            b.  Determine <x>, <x2>, and sx.

            c.  Determine <p>, <p2>, and sp.

            d.  Determine sxsp.  Is the uncertainty principle obeyed?

            e.  Determine A(k), the Fourier transform of y(x).

f.  Given that A*(k)A(k)dk is the probability that the wave number is between k and k + dk, determine <k>, <k2>, and sk.

            g.  Using the relation p = ћk, compare your results from (c) and (f).