(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine the normalization constant c in the wave function given by

[itex]\psi[/itex](x) = c cos(kx) exp[(-1/2)(x/L)^{2}]

2. Relevant equations

1=[itex]\int[/itex] |[itex]\psi[/itex](x)|^{2}dx

limits of integration being -inf to inf.

3. The attempt at a solution

I'm very much sure that my math is wrong, I'm very rusty with improper integrals.

1= [itex]\int[/itex] |c cos(kx) exp[(-1/2)(x/L)^{2}|^{2}dx

= [itex]\int[/itex] |c^{2}cos^{2}(kx) exp[-(x^{2}/L^{2})| dx

it's at this point I start getting into trouble

= c^{2}[itex]\int[/itex] |cos^{2}(kx) exp[-(x^{2}/L^{2})| dx

= c^{2}[itex]\int[/itex] cos^{2}(kx)dx [itex]\int[/itex] exp[-(x^{2}/L^{2})dx

= c^{2}(lim((2kx+sin(2kx))/4k)) ([itex]\pi[/itex])^{1/2}/(1/L^{2})^{1/2}

I think I'm pretty solidly wrong by this point... where did I go wrong?

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# Homework Help: Determining Normalization Constant

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