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Eigenfunctions and Energies for Sloped-Bottom Square-Well Potential

potential x
0
0
potential slope s
1
quantum level n
1
ψ
n
&
(0)
ψ
n
Δψ
V(x)
ψ
n
(0)
ψ
n
Eigenenergies
E
n
and eigenfunctions
ψ
n
of the potential
V(x)=s|x-
x
0
|
for
x1/2
and
V(x)=
for
x>1/2
are obtained numerically. This is treated as a perturbation of the infinite square-well potential, with
s=0
,
V(x)=0
for
x1/2
and
V(x)=
for
x>1/2
. The
th
n
eigenfunction of the unperturbed problem is denoted by
(0)
ψ
n
. Note that, for increasing quantum number
n
, the effect of the perturbation diminishes.
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