# Quantum Physics A(k) to psi(x)

1. Sep 10, 2008

### Felicity

1. The problem statement, all variables and given/known data

this problem is from (chapter 2 problem 1, gasiorowicz, quantum physics) where I am given
A(k) = N/(k2+a2) and must calculate psi(x)

2. Relevant equations

I am using the equation
psi(x,t) = integral from - infinity to + infinity A(k) ei(kx-wt) dk

which when t=0 goes to

psi(x,t) = integral from - infinity to + infinity A(k) eikx dk

3. The attempt at a solution

integral from - infinity to + infinity of
N/(k2+a2) * eikx dk

is this a good approach? How can I solve the integral?

any help would be greatly appreciated

thank you

2. Sep 10, 2008

### nrqed

yes it is the right approach.
just write
k2 + a2 as (k+ia)(k-ia)
and then do the integral in the complex k plane, closing above the real k axis so that eikx goes to zero and use the residue theorem

3. Sep 11, 2008

### Felicity

Thank you so much! would the residue then be e-ax/2ai ?