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PHYS126 Fall 2011
HW #8
Due 01 April
1)
Show that the following function of general sinusoidal wave
)
cos(
)
sin(
)
(
kx
b
kx
a
x
+
=
ψ
is equivalent to the following expression
ikx
ikx
Be
Ae
x
−
+
=
)
(
.
Please also give expressions for A and B in terms of
a
and
b
. [Note:
k
is a real number.
There is no restriction on
a
and
b
]
[
ikx
e
,
ikx
e
−
,)
sin(
kx
cos(
kx
and their arbitrary linear combination all are solutions to the
equation
)
(
)
(
2
2
x
k
x
dx
d
−
=
, but only two of them are independent.]
2)
Show that the following function of general sinusoidal wave
)
cos(
)
sin(
)
(
kx
b
kx
a
x
+
=
is equivalent to the following expression
}
Im{
)
sin(
)
(
)
(
φ
+
=
+
=
kx
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This note was uploaded on 03/31/2011 for the course PHY 126 taught by Professor Hobunchan during the Spring '11 term at HKUST.
 Spring '11
 HoBunCHAN
 Physics

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