Question

The wave function for a certain particle is 𝛹 = 𝐴cos2𝑥 𝑓𝑜𝑟 − 𝜋

2 < 𝑥 < 𝜋

2

Find the value

of A.

Answer 1

𝛹 = 𝐴cos2𝑥 𝑓𝑜𝑟 – 𝜋/2 < 𝑥 < 𝜋/2

Using normalization condition        [ lower limit =– 𝜋/2, upper limit = 𝜋/2]

$\smallint$|𝛹|² dx =1

A² $\intop$cos²2xdx =1

A²$\smallint$(1+cos4x) dx =2

A² [x] =2

A² [𝜋]=2

A² 𝜋 =2

    (ANSWER)