Many Particle in a one dimensional box

[dev70]

Hi pf,

I am just wondering how would the system be if i keep say 5 particles in a 1-D box. How would the wave functions be? Will quantum superposition happen? Entanglement? What about the energy levels? How would they be quantized? In short i want to know how would you solve the Schrödinger's Equation in a many particle 1-D box?

 

[craigi]

Try this:
http://galileo.phys.virginia.edu/classes/252/symmetry/Symmetry.html

 

[wotanub]

You're crossing into the regime of statistical mechanics.

Are the particles distinguishable?
Do they interact? How?
How big is the box?
etc.

 

[dev70]

What if we consider two cases in which particles are identical and other in which they are not (distinguishable )? And as far as the box is considered, we may take any length say 'a' but in one dimension only.

 

[craigi]

What if we consider two cases in which particles are identical and other in which they are not (distinguishable )? And as far as the box is considered, we may take any length say 'a' but in one dimension only.

Elementary particles are treated as indistinguishable in quantum mechanics, provided that they are of the same type.

Did you follow the link that I posted? It explains the problem well.

 

[ftr]

http://en.wikipedia.org/wiki/Fermi_energy

http://en.wikipedia.org/wiki/Fermi_level