# Electron in a 1-D box. Quantum Numbers

1. Nov 5, 2011

### teroenza

1. The problem statement, all variables and given/known data

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).

2. Relevant equations

One-D particle in a box energies

E= $\frac{pi*2*hbar^2}{2mL^2}$*n^2

m is the mass
L is the box's length

3. The attempt at a solution

I think my biggest question is, do the l and $m_{l}$ 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