# Particle in a box

## Homework Statement

(a)Think of a one-dimensional box of length L. There are two identical, non classical particles of mass m in the box. The total energy of the system is 13*pie^2h^2/2mL^2. What states are occupied by by the two particles?
(B) If a single non-classical particle of mass m in a two dimensional square box of side length L has energy 10pie^2h^2/2mL^2 what state is it in?
(C) Are the states found in A and B degenerate or nondegenerate?
(d) What is the maximum number of particles that can be in each state?

## The Attempt at a Solution

(a) I was able to find the energy levels to be n1=2 and n2=3 but what do they mean by states? Are you not supposed to have orbital quantum number and ml and ms? and why is that?

(b) since it is a two dimensional box it has two directions nyf= 3 or 1 and nxf=1 or 3. The energies should add since it is a 2 dimensional box correct?
(c) i have no idea what degenerate means. My teacher tells us that both a and b are degenerate. Is this because they have different energy levels? he said it has something to do with wave function.
(d) no idea think its either boson or fermion but not sure how to know without knowing wave function.

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(a) I was able to find the energy levels to be n1=2 and n2=3 but what do they mean by states? Are you not supposed to have orbital quantum number and ml and ms? and why is that?
You can also have n1=3 and n2=2. And states are defined by the quantum numbers, so |2,3> is a state as well as |3,2>. You don't have orbital quantum numbers because this is a 1D problem.

(c) i have no idea what degenerate means. My teacher tells us that both a and b are degenerate. Is this because they have different energy levels? he said it has something to do with wave function.
Degenerate just means that more than one state has the same energy. And both (a) and (b) have two possible states for the given energies.

(d) no idea think its either boson or fermion but not sure how to know without knowing wave function.
Does it specify somewhere that they are bosons or fermions?

when i asked him he said their are two kinds of particles. the normal one's we think of and then their are these other ones. So i am assuming they are bosons and fermions.

anyone know how to do part d?