Normalization of time independent wave function

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Homework Help Overview

The discussion revolves around normalizing a time-independent wave function, specifically \(\Psi(x) = A \cos(\pi x/a)\). Participants are exploring the process of determining the normalization constant \(A\) to satisfy the normalization condition of wave functions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the normalization condition, with one attempting to derive the expression for \(A\) but expressing uncertainty about their approach. Another participant questions the definition of normalization, while others inquire about the limits of integration necessary for the normalization process.

Discussion Status

The discussion is ongoing, with participants providing guidance on the normalization process and questioning the setup of the problem. There is an emphasis on clarifying the limits of integration, which is crucial for proceeding with the normalization.

Contextual Notes

There is a focus on the need for definite limits of integration for the normalization of the wave function, indicating that the wave function may be defined over a specific range of \(x\). Participants are addressing the implications of using indefinite integration in this context.

Skullmonkee
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Homework Statement


normalize the wave function [tex]\Psi(x)= Acos(\Pi*x/a)[/tex] to show that A=[tex]\sqrt{2/a}[/tex]

The Attempt at a Solution


i don't know how to get that answer as all i can tell, normalizing gives:
[tex]-A^{2}pi^{2}2x/a^{2} * sin (pix/a)[/tex]

However this does not give the right answer for A
Any help pointing out what I've missed would be great.
 
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Hi Skullmonkee,

Let me ask you a question first:

What expression "defines" the normalization of a wavefunction?
 
Do you mean this?

[tex]\int\Psi^{*}\Psi dx=1[/tex]

[tex]\int Acos(\pi x/a)*Acos(\pi x/a)dx[/tex]

= [tex]\int A^{2}cos^{2}(\pi x/a)[/tex]

But I am not sure where to go from here?
 
What are the limits of integration? I.e., over what range of x is the wavefunction defined?
 
You need to plug in the limits of integration. You can't normalize a wave function using indefinite integration.
 

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