(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant 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.

3. 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 offiveparticles, and how do I find the energy from here?

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

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# Homework Help: Shrodinger Equation for Multiple Particles

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