What is the box in particle in a box?

[mishima]

Hi, I am trying to demonstrate the relation between quantization of energy and wavelengths in a confined box for high school chemistry students. I am following an approach found in Atkins' "Chemical Principles". Anyways, its quite understandable, but I get the feeling maybe the box isn't actually what I think it is. I've been thinking of the box as the energy level (shell). But is it actually the orbital? Or something else entirely? Thanks.

 

[mishima]

Is this a bad question? I understand its just a model, but what is the box analogous to for say, an atom of hydrogen?

 

[DrDu]

A one dimensional box is a potential V(x) which is infinite for e.g. x<0, zero for x>=0 and x<=L and again infinite for x>L.
It is not an energy level. The energies and orbitals arise when you solve the Schroedinger equation for a particle moving in that potential.

 

[kith]

The box is really just a box: a volume with walls which are impenetrable for the particle. Although this is a valid approximation for some real physical systems, it is primarily a Gedankenexperiment which is easy to calculate and illustrates the behaviour of quantum mechanical systems. Especially, it is a quite bad model for atoms because they have no sharp boundary like the box.