- #1

mattmatt321

- 7

- 0

## Homework Statement

Five identical non-interacting particles are placed in an infinite square well with width L = 1 nm. I am asked to find the energy of the system if the particles are electrons.

## Homework Equations

The time-independent Schrodinger equation for a system of two particles, both with the same mass 'm' is:

-h(bar)

^{2}/2m * (d

^{2}[tex]\psi[/tex](x

_{1}x

_{2}/ (d

^{2}x

^{2}

_{1})) - h(bar)

^{2}/2m * (d

^{2}[tex]\psi[/tex](x

_{1}x

_{2}) / (d

^{2}x

^{2}

_{2})) + V[tex]\psi[/tex](x

_{1}x

_{2}) = E[tex]\psi[/tex](x

_{1}x

_{2})

All derivatives are partials.

Also, energy E

_{n}= -13.6(Z

^{2}/ n

^{2})eV.

## The Attempt at a Solution

Alright so since the question specifies the particles do not interact, V = V

_{1}(x

_{1}) + V

_{2}(x

_{2}). As in regular Schrodinger equations, I want to solve where V = 0 and I can write [tex]\psi[/tex]

_{nm}(x

_{1}

_{2}) = [tex]\psi[/tex]

_{n}(x

_{1})[tex]\psi[/tex]

_{m}(x

_{2}). From here I'm stuck -- how do I solve for a system of

*five*particles, and how do I find the energy from here?

(sorry for the typo in the title, by the way)