Proving Behavior of Particle in Infinite Potential: Wave Function?

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SUMMARY

The discussion centers on proving the behavior of a particle in an infinite potential well, commonly referred to as a "particle in a box." Participants emphasize the importance of understanding the wave function associated with this model, which is foundational in quantum mechanics. Key resources include the Wikipedia page on "Particle in a Box" and various lecture notes that explain the infinite square well concept. The conversation highlights the complexities involved, such as the inability to define a momentum operator directly.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with Schrödinger's equation
  • Knowledge of wave functions and their properties
  • Concept of infinite potential wells in physics
NEXT STEPS
  • Study the "Particle in a Box" model in quantum mechanics
  • Explore the implications of wave function collapse
  • Research the mathematical formulation of the infinite square well
  • Learn about the momentum operator and its limitations in quantum systems
USEFUL FOR

Students and educators in physics, particularly those focusing on quantum mechanics, as well as researchers interested in the foundational concepts of wave functions and potential wells.

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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