Electron in a 1-D box. Quantum Numbers

  • Thread starter teroenza
  • Start date
  • #1
195
5

Homework Statement



Imaging an electron (s=1/2) confined in a one-dimensional rigid box/ What
are the degeneracies of its energy levels? Make a sketch of the lowest few levels,
showing their occupancy for the lowest state of six electrons confined in the same box.
(Ignore the Coulumb repulsion among the electrons).


Homework Equations



One-D particle in a box energies

E= [itex]\frac{pi*2*hbar^2}{2mL^2}[/itex]*n^2

m is the mass
L is the box's length

The Attempt at a Solution



I think my biggest question is, do the l and [itex]m_{l}[/itex] exist for a particle in a box. In atoms the electrons are "orbiting" and have these numbers associated with their angular momentum, but not in a box.

I know spin in intrinsic and have accounted for it. I know the particle's energy depends only on n, and so all sub-levels associated with one n value are at the same energy and thus degenerate.

My original solution has a table listing all possible n, l, m_l, and spin, but I now believe this is wrong. I think it should now perhaps include just n and spin. The exclusion principle will guide how I draw the electrons that are allowed to exist in the energies.

Thank you
 

Answers and Replies

Related Threads on Electron in a 1-D box. Quantum Numbers

Replies
3
Views
2K
  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
3K
Replies
0
Views
2K
Replies
6
Views
1K
Replies
1
Views
1K
  • Last Post
Replies
6
Views
5K
  • Last Post
Replies
1
Views
5K
  • Last Post
Replies
1
Views
1K
Top