Studying mathematical concepts of quantum mechanics, I have recently become familiar with the classical model of one-dimensional particle being scattered by a potential barrier.
As a mathematician, I didn't really have an idea of where such model might be applied in practice. But I have observed that the window beside me has some interesting characteristics similar to this model. I can see both through it, and my reflection in it - clearly some light particles pass through the glass, and others are reflected with unchanged velocity. The thicker the glass would be, the less particles would pass - which is also true for increasing potential barrier width. If I substituted glass with shiny metal, no visible light would pass through and more particles would be reflected, which resembles increasing the potential value in the barrier. And finally (as far as the mathematician I am knows) not all electromagnetic waves pass through glass - which also seems related, because the amount of particles passing through barrier depends on the wave velocity/frequency.
Is there actually some correlation between these models? Is the window semi-transparent behavior induced by this particular quantum scattering phenomena? Or maybe there is a more genera (universal) partial reflection model, that works both in the case of potential barrier and a glass window?