2006-11-29 Problem Set
Due Nov 29, 2006
Problem 1: Tipler 6-41
Problem 2: Tipler 6-42
Problem 3: Tipler 6-46
Problem 4:
In class this morning (Mon, 11/27) we discussed the case of the barrier potential (Tipler p.
278) only for the case where the energy of the particle is less than the height of the barrier,
E < V0. This problem does some exploration of the problem for the other case where the
particle energy is higher than the barrier height.
a) Write the equations for the wave function for this E > V0 case for the 3 regions shown
in Fig. 6-27, part (a). That is, write equations for this case that are analogous to Eq. (6-
74). Apply the boundary condition that the particle is incident from the left and there is
only a right-going wave on the right. Be sure to give the definitions of any new symbols
that you introduce.
b) If you were to carry through the calculation of the transmission coefficient for this
case, you would find Eq. (6-75) except that the hyperbolic sine (sinh) function is replaced
by the ordinary sine function (sin). Also, the constant α, which was defined for E < V0, is
replaced by a different quantity appropriate for the case E > V0, which you will figure out
when you solve part (a). Show that the transmission coefficient can take on the value T =
1, when the wavelength of the wave function in the well has certain very special ratios to
the width of the well. What are these ratios?
