Probabilistic interpretation of wave function

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Homework Help Overview

The discussion revolves around the probabilistic interpretation of a wave function for a particle confined between rigid walls in one dimension. The original poster presents the wave function \(\Psi(x) = A \sin(\frac{\pi x}{L})\) and seeks to determine the normalization constant \(A\) under the condition that the particle remains within the defined boundaries.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need to set the integral of the probability density equal to one over the limits of integration from 0 to \(L\). Questions arise regarding the evaluation of the integral and the meaning of the complex conjugate in the context of the wave function.

Discussion Status

Some participants have provided clarifications regarding the complex conjugate and the normalization condition. There is an acknowledgment that the integral must equal one, and the original poster is encouraged to evaluate the integral to find the appropriate value for \(A\). The discussion appears to be progressing with multiple interpretations being explored.

Contextual Notes

Participants are working within the constraints of the problem, focusing on the normalization of the wave function and the implications of the probabilistic interpretation. There is an emphasis on understanding the mathematical relationships without providing direct solutions.

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Homework Statement


a particle moving in one dimension between rigid walls separated by a distance L has the wave function \Psi(x)=Asin(\Pix/L), since the particle must remain between the walls, what must be the value of A?


Homework Equations





The Attempt at a Solution



Ok so I'm thinking that since the particle has to be between x=0 and x=1, i should set the probability function = to one for these limits on the integral. I'm really confused on how to do that though
 
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What must the following integral be equal to according to the probability interpretation of the wave function?

\int_0^L\Psi^*\Psi dx=?
 
1? to get psi* what do i do?

thanks
 
The star means complex conjugate: replaces all is with -is. In your case, \psi^* = A^* sin(\pi x / L), but you can takeA to be real, making \psi = \psi^*.
 
okay, thanks a lot
 
Yes, that integral is equal to 1. You now, need to evaluate that and figure out what A must be for that expression to be true.

(I have been busy today and I see I'm a little late to respond. I hope you were able to figure it out.)
 

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