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A normalized state is expanded in an orthonormal basis as
c
0
∣
0
⟩
+
c
1
∣
1
⟩
c_0|0\rangle + c_1|1\rangle
c
0
∣0
⟩
+
c
1
∣1
⟩
with
c
0
=
(
1
+
i
)
/
5
c_0 = (1+i)/\sqrt{5}
c
0
=
(
1
+
i
)
/
5
and
c
1
=
3
/
5
c_1 = \sqrt{3}/\sqrt{5}
c
1
=
3
/
5
. By completeness, what is
∣
c
0
∣
2
+
∣
c
1
∣
2
|c_0|^2 + |c_1|^2
∣
c
0
∣
2
+
∣
c
1
∣
2
?
5 (the shared denominator)
1
4
/
5
4/5
4/5
= 0.8
2
/
5
2/5
2/5
= 0.4
Check answer