Q1. Consider the finite square well potential shown in the following diagram: U(x) E> 0 L х -U, The potential is given by: for x<0 , x>L| = (x)N -U, for 0 < x < L A particle with energy E>0 is incident on this region from the left. Using the plane wave approximation for the particle: e¯k is a suitable general solution to the time-independent a) Show that Y = Ae™+B Schrödinger wave-equation (TISE) that applies in the region x < 0 and find the relationship between k and E in this region. b) By analogy to part (a) show that Y = Ce“'*+De¯k'x is a suitable solution to the 2m(E+U) TISE that applies in the region 0 L_write down the four equations arising from the boundary conditions that apply at and x=L .
Q1. Consider the finite square well potential shown in the following diagram: U(x) E> 0 L х -U, The potential is given by: for x<0 , x>L| = (x)N -U, for 0 < x < L A particle with energy E>0 is incident on this region from the left. Using the plane wave approximation for the particle: e¯k is a suitable general solution to the time-independent a) Show that Y = Ae™+B Schrödinger wave-equation (TISE) that applies in the region x < 0 and find the relationship between k and E in this region. b) By analogy to part (a) show that Y = Ce“'*+De¯k'x is a suitable solution to the 2m(E+U) TISE that applies in the region 0 L_write down the four equations arising from the boundary conditions that apply at and x=L .
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please answer part c only, thanks.
Transcribed Image Text:Q1. Consider the finite square well potential shown in the following diagram:
U(x)
E>0
L
The potential is given by:
for x<0 , x>L|
-U. for 0 <x < L
U (x) =
E>0is incident on this region from the left. Using the plane
A particle with energy
wave approximation for the particle:
a) Show that Y = Ae*+Be¬k* is a suitable general solution to the time-independent
Schrödinger wave-equation (TISE) that applies in the region x <0 and find the
relationship between k and E in this region.
b) By analogy to part (a) show that Y = C e**+De¯** is a suitable solution to the
|2m(E+U)
ik'x
TISE that applies in the region 0 <x <L_and show that k'=
c) Given that Y = F e is a suitable wave-function for the region x > L write
down the four equations arising from the boundary conditions that apply at x=0
and
x=L .
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