Why does infinite potential well give rise to standing wave?

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SUMMARY

The discussion centers on the phenomenon of standing waves in an infinite potential well, specifically addressing why only standing waves can exist in such a scenario. It is established that the infinite potential well prevents the wave function from penetrating the walls, resulting in a zero probability of finding the particle outside the well. This leads to the conclusion that the wave function must vanish at the boundaries, defining the standing wave condition. The concept is clarified as an idealization rather than a generalization, acknowledging that while tunneling is theoretically possible, it is negligible in this context.

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  • Quantum mechanics fundamentals
  • Understanding of wave functions
  • Concept of potential wells
  • Knowledge of standing waves and their properties
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Students and professionals in physics, particularly those focused on quantum mechanics, wave phenomena, and theoretical physics. This discussion is beneficial for anyone seeking to deepen their understanding of wave functions and potential wells.

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For a particle in a box that is described with a wave function, why can there only be a standing wave when there is an infinite potential well? From my understanding, the infinite potential well makes it impossible for the particle to tunnel through the barrier and so the wave function cannot permeate the walls and there is a zero probability of finding the particle on the other side. Is this why there is a standing wave bounded by the walls?

Since we could never have an infinite potential well (That I know of?) does this mean that this is just a generalization and that this is always a probability of finding the particle outside the box?

Can someone let me know if I'm on the right track?

Thanks
 
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Yes you are. Since the wave function must exactly vanish on the edges of the well this is, by definition, a standing wave since the total length will always be a multple of \lambda/2. Moreover, yes, this is a generalization. The probability of tunneling outside the well will always be finite, even if extremely small in many cases.
 
The proper word is "idealization", not "generalization."
 

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