Deriving Wave Function: Confused about (ix/a) & (-x^2/2a)?

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The discussion centers on deriving the time-independent wave function and confusion surrounding the terms (ix/a) and (-x^2/2a). Participants suggest changing variables to k' = k - k0 and completing the square to clarify the derivation. There is uncertainty about where to substitute k' in the process, prompting requests for further guidance. One participant notes that this derivation resembles a Fourier transform of a Gaussian function. The conversation highlights the need for clearer steps in the derivation process.
sus1234
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Homework Statement
Trying to understand how the time independent wavefunction is derived from this
Relevant Equations
?
1644783404516.png


It is asking to derive the time-independent wave function and has managed to get the answer of
1644783451034.png

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

Thanks.
 
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The answer's wrong.

First, change variables to ##k' = k-k_0##, and then complete the square.
 
vela said:
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
 
sus1234 said:
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?
 

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