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

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Homework Help Overview

The original poster is attempting to derive the time-independent wave function and expresses confusion regarding the terms (ix/a) and (-x^2/2a) in their answer.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Some participants question the correctness of the original answer and suggest changing variables to k' = k-k_0 and completing the square. Others inquire about the appropriate substitution for k' and seek further guidance on the integration process.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and offering suggestions for variable changes. There is no explicit consensus on the correct approach, but guidance has been requested regarding the integration and variable substitution.

Contextual Notes

Participants are discussing the derivation in the context of quantum mechanics, specifically relating to wave functions and transformations, with references to Fourier transforms and Gaussian functions.

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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