Normalizing Constant 3D Infinite Well

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Discussion Overview

The discussion centers on the normalization of the wave function for a three-dimensional infinite potential well, specifically addressing the normalization constant A in the context of the time-independent Schrödinger equation. Participants explore the mathematical requirements for normalization and the implications for the probability density of the wave function.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant presents the wave function and asks how to normalize the constant A to achieve a specific value.
  • Another participant explains that a normalized state means the total probability described by the wave function must equal one.
  • A participant suggests that if A is set to (2/L)^3/2, then the probability density would equal one, implying a straightforward approach to solving for A.
  • It is noted that the integral of the square of the wave function over the entire volume of the well must equal one for normalization.
  • One participant questions the earlier suggestion about solving for A, indicating a need for clarification based on previous comments.
  • A participant expresses that they received clarification during office hours, indicating a better understanding of the normalization process.

Areas of Agreement / Disagreement

Participants exhibit some agreement on the concept of normalization and its requirements, but there is uncertainty regarding the specific steps to solve for the normalization constant A. The discussion does not reach a consensus on the method to derive A.

Contextual Notes

Participants do not fully resolve the mathematical steps involved in the normalization process, and there are varying interpretations of how to approach solving for A.

RaulTheUCSCSlug
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For time independent Schrödinger's equation in 3-D

Where Enx,ny,nz=(nx/Lx2+ny/Ly2+nz/Lz2)(π2ħ2/2m
and Ψnx,ny,nz=Asin(nxπx/Lx)sin(nyπy/Ly)sin(nzπz/Lz)

How do I normalize A to get (2/L)^3/2?

I don't think I understand how to normalize constants.
 
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A normalized state ##\psi## means that the total probability described by this state, ##|\psi|^2##, is equal to unity.
 
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So when A is (2/L)^3/2 then |\psi|^2 is equal to one since the probability density must go to one?

So to solve for A one would just go through |\psi|^2 = 1 then solve for A?
 
The integral of ##|\psi^2|## over all space (or equivalently, over the entire volume of the well, since ##\psi## must be zero outside the well) must equal 1 in order for ##\psi## to be normalized.
 
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RaulTheUCSCSlug said:
So to solve for A one would just go through |\psi|^2 = 1 then solve for A?
No, not that which must be equal to 1. Take a look at jtbell's comment above.
 
Right. So the purpose is to have the probability of the whole function sum up to 1. Okay. I went to office hours and got things clarified thank you!
 

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