Where do the (ix/a) and (-x^2/2a) terms come from in this wave function derivation?

[sus1234]

Homework Statement

Trying to understand how the time independent wavefunction is derived from this

Relevant Equations

?

It is asking to derive the time-independent wave function and has managed to get the answer of

and i am very confused as where (ix/a) and (-x^2/2a) came from ?

Thanks.

 

[vela]

The answer's wrong.

First, change variables to $k' = k-k_0$, and then complete the square.

 

[sus1234]

The answer's wrong.

First, change variables to $k' = k-k_0$, and then complete the square.

Hi,

Thank you for your reply, I'm not sure where I'm meant to sub in k' = k-k0, could you provide more guidance ?

thanks

 

[vela]

Thank you for your reply, I'm not sure where I'm meant to sub in k' = k-k0, could you provide more guidance ?

You've never changed the variable of integration?

 

[PhDeezNutz]

Isn’t this just a Fourier transform of a Gaussian?

https://quantummechanics.ucsd.edu/ph130a/130_notes/node88.html