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Problem Set for Barrier Potential with E > V0, Assignments of Physics

This problem set focuses on the barrier potential problem where the energy of the particle is greater than the height of the barrier. Students are required to write the equations for the wave function in the three regions shown in fig. 6-27 and apply the boundary condition. They will also calculate the transmission coefficient and find the special ratios of the wavelength to the width of the well that allow t = 1.

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Pre 2010

Uploaded on 08/17/2009

koofers-user-pql
koofers-user-pql 🇺🇸

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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?

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2006-11-29 Problem Set

Due Nov 29, 2006

Problem 1: Tipler 6-

Problem 2: Tipler 6-

Problem 3: Tipler 6-

Problem 4:

In class this morning (Mon, 11/27) we discussed the case of the barrier potential (Tipler p.

  1. only for the case where the energy of the particle is less than the height of the barrier, E < V 0. 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 > V 0 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 < V 0 , is replaced by a different quantity appropriate for the case E > V 0 , 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?