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 E_n = -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)

 

[nickjer]

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