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## 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