Particle in a box with one finite wall and one infinite wall

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SUMMARY

This discussion focuses on the quantum mechanics of a particle confined in a square potential well with one finite wall and one infinite wall. The energy levels are described by the equation E[n] ~ (n*pi*(ħ))²/(2m(L+2d)²), where the participant questions whether to replace the term 2d with 1d due to the nature of the infinite wall. The conversation explores the implications of this configuration on the particle's behavior compared to standard finite and infinite square wells, emphasizing the importance of boundary conditions in quantum systems.

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EnSlavingBlair
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Hello all, I came across what I think is a very interesting question the other day;

How would you treat a particle trapped in a square well that had one finite wall and one infinite wall? Say for En~(n*pi*(h-bar))2/(2m(L+2d)2) would you replace the 2d by 1d? As you can only find the infinite 'wall' outside one of the walls? And what affects would it have on other areas, in comparison to either a normal finite square well or an infinite one?
 
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Treat it as a finite wall and take only the odd solutions.
 
nSlavingBlair said:
Hello all, I came across what I think is a very interesting question the other day;

How would you treat a particle trapped in a square well that had one finite wall and one infinite wall? Say for En~(n*pi*(h-bar))2/(2m(L+2d)2) would you replace the 2d by 1d? As you can only find the infinite 'wall' outside one of the walls? And what affects would it have on other areas, in comparison to either a normal finite square well or an infinite one?


I don't understand what you are describing ... are you talking about an infinite well with a narrower finite well at the bottom? Are you talking about a case where, say, the left hand wall is infinite and the right hand wall is finite? Or something else altogether?
 
So you could think of it similar to a closed cylinder air column, with a node at the closed end (infinite wall) and an antinode at the open end (finite wall)?
 
SpectraCat said:
Are you talking about a case where, say, the left hand wall is infinite and the right hand wall is finite?

That is exactly what I mean, sorry if my explanation was ambiguous.
 

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