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).