Proving Behavior of Particle in Infinite Potential: Wave Function?

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Discussion Overview

The discussion revolves around the behavior of a particle subjected to an infinite potential, specifically in the context of quantum mechanics. Participants explore the existence and description of the wave function for a particle in an infinite potential well, often referred to as a particle in a box.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant inquires about proving the behavior of a particle in an infinite potential and whether the wave function exists.
  • Another participant seeks clarification on whether the original question pertains to a particle in a box or an infinite potential well.
  • A participant confirms the scenario as a particle in a box and asks how to describe the wave function in this context.
  • There is a suggestion to refer to a Wikipedia link that may provide a satisfactory answer to the original question.
  • One participant mentions the interest in wave functions and their collapse, indicating a broader conceptual interest.
  • Another participant notes that the term "infinite square well" is commonly used and suggests that many introductory resources on quantum mechanics cover this example.
  • A later reply highlights potential subtle problems associated with the infinite square well model, such as the inability to define a momentum operator but its square.

Areas of Agreement / Disagreement

Participants generally agree on the context of the discussion being related to the infinite potential well, but there are multiple competing views regarding the complexities and subtleties involved in the model.

Contextual Notes

Some limitations include the potential for unresolved mathematical steps and the dependence on definitions related to the wave function and momentum operator in this context.

loversphisics
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Hello, guys! I have a question. How can I prove the behavior of a particle subjected to an infinite potential? Will the wave function exist?
 
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Welcome to PF.

loversphisics said:
Hello, guys! I have a question. How can I prove the behavior of a particle subjected to an infinite potential? Will the wave function exist?
Do you mean like a particle in a box? A particle in an infinite potential well? Can you be more specific? Thanks.

https://en.wikipedia.org/wiki/Particle_in_a_box
 
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berkeman said:
Welcome to PF.Do you mean like a particle in a box? A particle in an infinite potential well? Can you be more specific? Thanks.

https://en.wikipedia.org/wiki/Particle_in_a_box
Yes! It´s like a particle in a box. Do you how can i describe the wave function to this exemple ? Where do i start to solve this question ?
 
loversphisics said:
Yes! It´s like a particle in a box. Do you how can i describe the wave function to this exemple ? Where do i start to solve this question ?
Did you read the Wikipedia link that I posted? That should answer your question pretty well.
 
berkeman said:
Did you read the Wikipedia link that I posted? That should answer your question pretty well.
IMG! I hadn't seen the link above. I'll read it and anything I'll come here. Thank you very much.
 
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Wave functions are interesting. Even more so their collapse.
 
Another common term for this situation is "infinite square well." If you Google for this phrase you will find many lecture notes about it. I think almost every introduction to quantum mechanics by way of Schrödinger's equation starts with this example. :smile:
 
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Yes, and almost any introduction hides the subtle problems of this only apparently simple example. E.g., you cannot define a momentum operator but its square (and thus the Hamiltonian used to define the model)...
 
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