Re: [Phys-L] Infinite square well experimental data?

["Daniel V. Schroeder" <dschroeder@weber.edu>]

John Denker said:

> I don't see that as truly essential;  that depends on an additional
> assumption, namely energy proportional to k^2.  For electromagnetism
> including optics, and for sound, and for other massless excitations,
> the energy only goes like |k| to the first power.

Sorry, I should have clarified that the context here is the quantum mechanics of a single nonrelativistic particle, where students have just learned that the energy levels are proportional to the square of the quantum number n.

In this context, I think it's reasonable to look, in experimental data, for energy level spacing that increases with n, as a signal that the quantum well is reasonably deep and reasonably abrupt, so it can reasonably be modeled as an infinite square well.

Infinite square well data for relativistic particles or nondispersive quasiparticles might also be pedagogically useful, though in a somewhat different context.  The trick there, I think, is ensuring that we're measuring single-particle energies and not just frequencies that are more readily interpreted in terms of classical waves.

> *) I get almost 8000 hits from
>   
> https://www.google.com/search?q=%22quantum+dot%22+%22square+well%22

This remark is unhelpful and condescending.


Kyle Altmann said:

> I think the data in figure 2 of this paper does a great job of showing the 
> decrease in spacing in energy as the quantum number increases, as well as the 
> change in energy of a particular state with well thickness:
> "Quantum well states and short period oscillations of the density of states at 
> the Fermi level in Cu films grown on fcc Co(100) " P. Segovia, E.G. Michel, 
> J.E. Ortega Physical Review Letters 77 (16) (1996) 
> 3455-3458<tel:(1996)%203455-3458>.

I'm not seeing anything here that looks clean enough to serve the pedagogical purpose I have in mind.  I'm also perplexed by "decrease in spacing in energy as the quantum number increases," which is backwards.  In the data I don't see a clear increase or decrease, but perhaps I'm not looking at it correctly.

Dan Schroeder
Physics Department
Weber State University