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An unnormalized wavefunction on
0
≤
x
≤
1
0 \le x \le 1
0
≤
x
≤
1
is
ψ
(
x
)
=
A
x
(
1
−
x
)
\psi(x) = A x(1-x)
ψ
(
x
)
=
A
x
(
1
−
x
)
, and zero outside. Using
∫
0
1
x
2
(
1
−
x
)
2
d
x
=
1
/
30
\int_0^1 x^2(1-x)^2 \, dx = 1/30
∫
0
1
x
2
(
1
−
x
)
2
d
x
=
1/30
, find the normalization constant
A
A
A
(take
A
>
0
A > 0
A
>
0
).
🔬 try it before you answer
1
/
30
≈
0.0333
1/30 \approx 0.0333
1/30
≈
0.0333
30
30
≈
5.477
\sqrt{30} \approx 5.477
30
≈
5.477
1
/
30
≈
0.183
\sqrt{1/30} \approx 0.183
1/30
≈
0.183
Check answer