# Shrodinger Equation for Multiple Particles

• mattmatt321

## 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 * (d2$$\psi$$(x1x2 / (d2x21)) - h(bar)2/2m * (d2$$\psi$$(x1x2) / (d2x22)) + V$$\psi$$(x1x2) = E$$\psi$$(x1x2)

All derivatives are partials.

Also, energy En = -13.6(Z2 / n2)eV.

## The Attempt at a Solution

Alright so since the question specifies the particles do not interact, V = V1(x1) + V2(x2). As in regular Schrodinger equations, I want to solve where V = 0 and I can write $$\psi$$nm(x12) = $$\psi$$n(x1)$$\psi$$m(x2). 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)

Do you know how to solve it for a system of 2 noninteracting particles? It is treated exactly the same way for 5 particles.