Problem with normalisation, or should i say integration

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Homework Help Overview

The discussion revolves around the normalization of a wave packet described by the function \(\psi(x) = Ce^{i\omega x}e^{-\left|x\right|/2\Delta x}\), where \(C\) is a normalization constant. Participants are tasked with normalizing this function to unity.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants express uncertainty regarding the integration of the expression involved in the normalization condition, specifically \(\left|C\right|^{2}\int e^{-\left|x\right|/\Delta x} dx = 1\). Some participants mention feeling lost and question how to handle the integration.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts and expressing confusion about the integration process. There is acknowledgment of the difficulty of the problem, and some participants refer to guidance received from a professor, indicating that there may be different perspectives on how to approach the normalization.

Contextual Notes

Some participants note variations in the expression, such as redefining \(\Delta x\) in terms of \(x - x_0\), which may introduce additional complexity to the problem.

spaghetti3451
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Homework Statement



Consider the wave packet [itex]\psi(x)\equiv ψ(x, t = 0) = Ce^{i\omega x}e^{-\left|x\right|/2\Delta x}[/itex] where C is a normalisation constant.

Normalise [itex]\psi(x)[/itex] to unity.

Homework Equations



The Attempt at a Solution



I know the normalisation condition. My problem is when I have ...

[itex]\left|C\right|^{2}\int e^{-\left|x\right|/\Delta x} dx = 1[/itex]

Any help will be MUCH appreciated.
 
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failexam said:

Homework Statement



Consider the wave packet [itex]\psi(x)\equiv ψ(x, t = 0) = Ce^{i\omega x}e^{-\left|x\right|/2\Delta x}[/itex] where C is a normalisation constant.

Normalise [itex]\psi(x)[/itex] to unity.

Homework Equations



The Attempt at a Solution



I know the normalisation condition. My problem is when I have ...

[itex]\left|C\right|^{2}\int e^{-\left|x\right|/\Delta x} dx = 1[/itex]

Any help will be MUCH appreciated.


Say delta x=x-x0
 
Good thinking! But this makes the problem even harder . lolzz. because I have literally NO idea how to integrate such an expression!
 
failexam said:
Good thinking! But this makes the problem even harder . lolzz. because I have literally NO idea how to integrate such an expression!

Thank U! I just got lost like U did, but my professor gave this idea.
 

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