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Mixed state in infinite well

Mixed state in infinite well

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bf (a) rm

The normalization condition for the function is
$$
1 = int_{-a/2}^{a/2} |Psi(x)|^2 dx
= |A|^2 int_{-a/2}^{a/2} l( cos{pi xover a} - sin{2pi xover a} r)^2 dx =
$$
$$
= |A|^2 int_{-a/2}^{a/2}
l( cos^2{pi xover a} - 2cos{pi xover a}sin{2pi xover a}
+ sin^2{2pi xover a}r) dx =
$$
$$
= |A|^2 l( {aover 2} + 0 + {aover 2} r) = a|A|^2.
eqno(2.1)
$$
Therefore
$$
A = {1over sqrt{a}}
eqno(2.2)
$$
would make $Psi$ ...

$2.19