- #1
atomicpedals
- 209
- 7
Homework Statement
Determine the normalization constant c in the wave function given by
[itex]\psi[/itex](x) = c cos(kx) exp[(-1/2)(x/L)2 ]
Homework Equations
1=[itex]\int[/itex] |[itex]\psi[/itex](x)|2 dx
limits of integration being -inf to inf.
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] |c2 cos2(kx) exp[-(x2/L2)| dx
it's at this point I start getting into trouble
= c2 [itex]\int[/itex] |cos2(kx) exp[-(x2/L2)| dx
= c2 [itex]\int[/itex] cos2(kx)dx [itex]\int[/itex] exp[-(x2/L2)dx
= c2 (lim((2kx+sin(2kx))/4k)) ([itex]\pi[/itex])1/2/(1/L2)1/2
I think I'm pretty solidly wrong by this point... where did I go wrong?