Solve Schrodinger Equations: Fourier Series/Integral for Psi(x)

[physicsg]

Homework Statement

Suppose the wave function for a particle of mass m in one dimension is
psi(x)= (const)e^x2/4l2

express this wave function in terms of a Fourier series or integral.

I know that psi(x)=$\sum$_k (a_k *e^ikx) for a plane wave. I have no idea where to go from here. Any help is appreciated. I don't even know what the L in the wave function represents. Psi(x) should look like a gaussian curve.

 

[vela]

You're missing a negative sign in the exponent. It should be $$\psi(x) \propto e^{-\frac{x^2}{4l^2}}$$If you express it as a Fourier integral, you have$$\psi(x) = \frac{1}{2\pi}\int_{-\infty}^\infty f(k)e^{ikx}\,dk$$You need to figure out what f(k) is.