Can This Integral Be Simplified?

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Homework Help Overview

The discussion revolves around the simplification of the integral ∫∞-∞|∂Ψ/∂x|²dx, which is related to wavefunctions in quantum mechanics. Participants are exploring whether this integral can be simplified and what implications arise from properties of the wavefunction.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the potential for simplification of the integral and question whether properties of normalized wavefunctions affect the derivative. There is mention of integration by parts as a possible approach and consideration of specific examples like Gaussian wavefunctions.

Discussion Status

The discussion is ongoing, with participants raising questions about assumptions related to normalization and the implications for the integral. Some guidance has been offered regarding integration techniques and examples to consider, but no consensus has been reached.

Contextual Notes

There is a mention of the original problem being tied to the expression E = (1/2m) , which may influence the discussion but is not fully explored. The original poster has not attempted any specific methods yet.

Erik 05
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Homework Statement


∫∞-∞|∂Ψ/∂x|2dx

Homework Equations



Can this be simplified at all

The Attempt at a Solution

 
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What have you tried?
 
I haven't tried anything. The question, you are given E = (1/2m) <pΨ|pΨ> and asked to express it in ∂Ψ/∂x, so it may be fine just to leave it as the above. I was just thinking that maybe there is a 'standard' simplification for that integral. For example if Ψ is normalized, does that imply ∂Ψ/∂x also is? Well probably not, but would it simplify the integral somehow?
 
Last edited:
If you are talking about a general wavefunction, then your original expression is as simple as anything else. You can,of course, try integration by parts - which should lead back to an alternative version of the inner product as well.

Erik 05 said:
For example if Ψ is normalized, does that imply ∂Ψ/∂x also is?

That's definitely something you should explore for yourself. A Gaussian is often a good example to start.
 
Ok, thanks.
 

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