Normalize Wave Function: Find A Value

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Discussion Overview

The discussion revolves around finding the normalization constant A for the wave function Ψ = Axe ^ (-x squared/2). Participants explore the process of normalization, particularly the integration limits and the mathematical steps involved.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant asks how to find the normalization constant A and whether to integrate from negative to positive infinity since no other limits are specified.
  • Another participant confirms that if unspecified, the integration should indeed be from negative to positive infinity.
  • A third participant proposes a specific form of the integral to evaluate, suggesting it leads to an expression involving the wave function's form.
  • A later reply clarifies the correct approach to find A, indicating the need to evaluate the integral of the product of the wave function and its complex conjugate, leading to a specific integral involving x squared and an exponential function.

Areas of Agreement / Disagreement

Participants generally agree on the need to integrate from negative to positive infinity, but there is no consensus on the specific steps or expressions to use in the normalization process.

Contextual Notes

Some participants' statements depend on assumptions about the wave function's form and the evaluation of integrals, which may not be fully resolved in the discussion.

CollectiveRocker
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How do I find the value of the normalization constant A for the wave function
Ψ = Axe ^ (-x squared/2)? I know that I set it equal to 1, but do i do the integral from negative infinity to positive infinity; for no other limits are given?
 
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Sounds like this very same question has been asked before...that time with the square of the W.f'n. being the given qty...

Yes, if unspecified, integrate from negative to positive infinity.
 
So do I just end up with: ((-x squared)/2)Axe ^(-x squared/2), evaluated from negative infinity to infinity?
 
No, you want to find A from
[tex]\int_{-\infty}^{\infty} \psi ^* (x) \psi (x) dx = 1[/tex]

[tex]=> \frac{1}{|A|^2} = \int_{-\infty}^{\infty} x ^2 e^{-x^2} dx[/tex]
 
Last edited:

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