We study the one-dimensional wave equation with an inverse power potential that equals
c
o
n
s
t
.
x
−
m
const.x^{-m}
for large
|
x
|
|x|
, where
m
m
is any positive integer greater than or equal to 3. We show that the solution decays pointwise like
t
−
m
t^{-m}
for large
t
t
, which is consistent with existing mathematical and physical literature under slightly different assumptions.
Our results can be generalized to potentials consisting of a finite sum of inverse powers, the largest of which being
c
o
n
s
t
.
x
−
α
const.x^{-\alpha }
, where
α
>
2
\alpha >2
is a real number, as well as potentials of the form
c
o
n
s
t
.
x
−
m
+
O
(
x
−
m
−
δ
1
)
const.x^{-m}+O( x^{-m-\delta _1})
with
δ
1
>
3
\delta _1>3
.