The ground state of the infinite square wel

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Homework Help Overview

The discussion revolves around the ground state of the infinite square well and its properties, particularly whether it is an eigenfunction of momentum. Participants are exploring the implications of this question within the context of quantum mechanics.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • The original poster questions the relationship between the ground state and momentum eigenfunctions. Some participants suggest examining the mathematical representation of the ground state and applying the momentum operator to it. Others introduce a classical analogy to discuss momentum conservation in a quantum context.

Discussion Status

The discussion is active, with participants offering different perspectives on the question. There is an exploration of both mathematical and physical reasoning, and while some guidance has been provided, there is no clear consensus on the implications of the ground state regarding momentum.

Contextual Notes

One participant notes that the question may be more appropriate for the homework section of the forum, indicating potential constraints on the discussion's focus. Additionally, there is a caution against directly applying classical intuition to quantum scenarios.

ttiger654
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Is the ground state of the infinite square well an eigenfunction of momentum?? If so, why. If not, why not??
 
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You should take these kinds of questions to the homework section of the forum.
 
Write down the ground state in x representation and try the momentum operator on it. Do you get back a multiple of the ground state?
 
I think that Dick has adequately covered the mathematical aspect of it. Now let's think about some common sense physics. Imagine a classical ball bouncing elastically between two rigid walls (let's neglect gravity here). So kinetic energy is conserved at each collision, right? But the momentum is obviously not conserved, as the ball spends half its time going left and the other half going right. (Recall that momentum has direction).

Caveat: Normally, thinking of quantum particles as classical particles is ill advised, but this is one of those situations in which the classical result carries over to the quantum scale.
 

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