1. Consider a one-dimensional rectangular potential barrier V(x): V(2) – {v. So z(0, z)a 0(z(a (1) where Vo is positive. A particle with energy E < V, approaches the barrier from the left (see figure Fig. 1). E 3 x=a Figure 1 i Find in each region the wave function by solving the Schrodinger equation. ii By definition, the transmission coefficient T is defined as the transmitted current divided by the incident current: Jranamatted T Jmesdent where j 2mi evaluate T in terms of the amplitudes of transmitted and incident wave functions. iii Using the boundary conditions prove that: T = where ka 1+ sinh kya is the wave vector in region 2.
1. Consider a one-dimensional rectangular potential barrier V(x): V(2) – {v. So z(0, z)a 0(z(a (1) where Vo is positive. A particle with energy E < V, approaches the barrier from the left (see figure Fig. 1). E 3 x=a Figure 1 i Find in each region the wave function by solving the Schrodinger equation. ii By definition, the transmission coefficient T is defined as the transmitted current divided by the incident current: Jranamatted T Jmesdent where j 2mi evaluate T in terms of the amplitudes of transmitted and incident wave functions. iii Using the boundary conditions prove that: T = where ka 1+ sinh kya is the wave vector in region 2.
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Transcribed Image Text:1. Consider a one-dimensional rectangular potential barrier V(x):
z(0, r)a
0(r(a
V(x) -
(1)
where Vo is positive. A particle with energy E < V, approaches the barrier
from the left (see figure Fig. 1).
2
E
1
3
x=0
x=a
Figure 1
i Find in each region the wave function by solving the Schrodinger equation.
ii By definition, the transmission coefficient T is defined as the transmitted
current divided by the incident current:
T- İranamtted
Jimetdent
where j
2mi
(2)
evaluate T in terms of the amplitudes of transmitted and incident wave
functions.
iii Using the boundary conditions prove that: T =
where k2
1+E Ninh? kga
is the wave vector in region 2.
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