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HW #5 – Schrödinger Equation
Phys320 –Spring 2007 (Reshchikov)
p. 1
0
1 nm
Ψ
n = 4
0
Problem 1
(a)
Draw the wave function
of an electron confined to a 1nm wide infinite well for the
n
= 4 state.
(b)
Find the wavelength
λ,
momentum
p
(and
pc
), and energy
E
for the electron in this state (all in Modern
Units).
Alternatively:
22
2
2
6
2
26
(
)
(1240)
16
6.02
8
8
8 (0.511 10 )(1)
2
2(0.511 10 )6.02
6200
1240
0.2
6200
Kn
K
hh
c
EE
n
n
e
V
mL
mc L
pc
mc E
eV
c
nm
pp
c
λ
==
=
=
=
××
=
=×=
=
=
Problem 2
(a)
Draw the wave function
of an electron confined to a 0.5nm wide finite well for the n = 5 state.
(b)
Find the wavelength
λ
(nm)
,
momentum in terms of
pc
(eV), and energy E for the electron in this state.
Briefly describe how
ψ
(x) would change if the “walls” of the well were decreased in height.
()
2
6
5
20
.5nm
2
0.2 nm
55
1240 eV nm
6200 eV
0.2 nm
6200 eV
37.6 eV
.511 10 eV
n
L
pc
E
=
=
×
If the walls of the square well potential were decreased in height, then
ψ
(x) would decay slower
in the
regions outside the well. Number of peaks does not change. Amplitude slightly decreases due to
“leakage” of some portion of wave function inside the walls.
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 Spring '04
 Baski
 Physics, Energy, Momentum

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