Suppose there is a particle with mass m that is projected with energy E = V0 at the potential energy barrier defined in the provided images. Find the most general solution to the time independent Schrodinger equation in the regions x < 0, 0 < x < a, and x > a. Apply the appropriate boundary conditions and determine the transmission coefficient for a particle that is projected at the barrier from the left. Be sure that your result behaves appropriately in the limit a → 0.
Suppose there is a particle with mass m that is projected with energy E = V0 at the potential energy barrier defined in the provided images. Find the most general solution to the time independent Schrodinger equation in the regions x < 0, 0 < x < a, and x > a. Apply the appropriate boundary conditions and determine the transmission coefficient for a particle that is projected at the barrier from the left. Be sure that your result behaves appropriately in the limit a → 0.
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Suppose there is a particle with mass m that is projected with energy E = V0 at the potential energy barrier defined in the provided images.
Find the most general solution to the time independent Schrodinger equation in the regions x < 0, 0 < x < a, and x > a. Apply the appropriate boundary conditions and determine the transmission coefficient for a particle that is projected at the barrier from the left. Be sure that your result behaves appropriately in the limit a → 0.
(Note: The most general solution to a 2nd order differential equation has 2 arbitrary constants; this is true in each of the 3 regions defined in this problem.)
Transcribed Image Text:E
VA
0
Vo
a
X
Figure 4.39 A potential energy barrier of height Vo for
scattering of a particle with E = Vo.
Transcribed Image Text:0
x < 0
V(x) = Vo 0<x<a
x > a
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