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 s_x.

c. Determine <p>, <p²>, and s_p.

d. Determine s_xs_p. 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 s_k.

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

6-30

6-31

6-49